What did the letter theta symbolize in ancient Greece?

Theta is the 8th letter of the greek alphabet: uppercase Θ or ϴ, lowercase θ. Whether it symbolized anything is a matter related to the field of studies called Symbology. It can be rational or esoteric. In the latter case, anyone can believe in a meaning and there are and were many schools. Ergo: Greeks did not have a unique symbolization. What different symbolizations existed (and when ?) could be an interesting question. The same applies to today's many different meaning of any symbol.

The problem with symbols is that they need interpretation, but are almost never obvious, and subject to change over time, or even subject to contemporary contradiction.

One symbolic meaning is indeed for ‘death’ and thus called ‘theta nigrum’:

The interpretation of Θ in funerary epigraphy and documents on papyrus is problematic, as is shown by the fact that it has been the subject of an ongoing discussion and controversy.
In his Index to the first edition of CIL I Mommsen describes it as theta nigrum. This interpretation is supported by the literary evidence. Sources from different periods speak of the Greek letter Θ as a sign of death.
Mommsen's technical term, adopted later also by other modern scholars, comes from a passage of Persius. Martial calls a sign of death given by the quaestor the 'new theta'. Later, the Greek letter appears in one of Ausonius' six epigrams on the subject of the magister Eunus, a cunnilingus. The invective of this poem is based on the symbolism of Greek letters. […]

If that sounds ‘direct enough’, the very term “new theta” should give some pause.

Despite Isidore's assertion that theta was one of the 'mystic letters of the Greeks' (cf. above), we have no evidence for its use in Greek epigraphic sources. This has led some scholars to believe that the theta found in Latin inscriptions was indeed an O (= obitus), with a medial bar to mark the abbreviation as e.g. often in B (with a medial bar) for beneficiarius.

Mommsen was the first to adopt this idea, abandoning the view which he originally maintained in the Index to CIL I 17; he was followed by Mowat. But, as we shall see, such a conclusion cannot be drawn for Latin epigraphy in general. […]

In respect to the possible connection between Θ and obitus in epitaphs from Rome, it is important to note that the occurrences of obire (both in its past participle and as a finite verb, obiit) in inscriptions from the capital are not only comparatively rare, but also, as observed by Friggeri-Pelli (p. 171), later than the period of currency of Θ. I therefore see no justification for the assertion that the composers of epitaphs in Rome who used would have had in mind obitus. Indeed, the fact that, as already noted, it is in military (and gladiatorial) contexts and in official documents (fasti) that Θ survives epigraphically at a later date speaks further in favour of the interpretation of the symbol as the Greek letter; as we have seen, the symbolism of Θ = theta nigrum in such contexts is supported both by real-life documents (military papyri) and by literary sources (Persius, Martial, Ausonius, Rufinus, Isidorus). […]

In the absence of any evidence to the contrary, there is no reason to believe that the symbol on these occasions was anything else but the theta nigrum, the symbolism of which in the Roman world is confirmed by literary sources and documents on papyrus. On the other hand, a number of phenomena in Noricum suggest that in the imperial inscriptions in that province, Θ possibly originating as the Greek letter, might sometimes (if not always) have concealed the past participle of obeo, obitus.

— Iveta Mednikarova: "The Use of Θ in Latin Funerary Inscriptions", Zeitschrift für Papyrologie und Epigraphik, 2001, Bd. 136 pp. 267–276, 2001 jstor

But as already stated, ‘death’ is just one meaning associated with this. The often quoted but unsourced English Wikipedia entry on this is a plagiarised masonic interpretation. However, a real somehwat more ancient meaning attached to this does exist as well:

The meaning of Boethius's highly influential allegorical figure of Philosophy in his Consolation of Philosophy has been much discussed. The central linguistic fact is that she represents some form of wisdom or learning: philosophia, from philein, to love; and sophia, wisdom, means ‘the love ofwisdom.’ That this wisdom is recorded in her garment also remains unchallenged: Following a distinction made by Boethius himself, the Greek letters Π and Θ on Philosophy's famous robe are generally understood as symbols of practical and speculative philosophy, the letters for which begin with pi and theta, respectively. […]

The theta on the top hem of Philosophy's dress, aside from its symbolic role as an emblem of philosophical enlightenment, can also be seen as manifesting in material terms the ultimate in human loss: one's own imminent mortal absence. Henry Chadwick has pointed out that prison clothing during this period was marked with a theta for thanatos to symbolize the death penalty and thus the possibility that Boethius himself (author and protagonist) was wearing a theta.

— Andrea Denny-Brown: "How Philosophy Matters: Death, Sex, Clothes, and Boethius", in: E. Jane Burns (ed): "Medieval Fabrications. Dress, Textiles, Clothwork, and Other Cultural Imaginings", Palgrave Macmillan: New York, Basingstoke, 2004.

A medieval variant representation for this:

— Codex Vindobonensis Palatinus 242

The meaning of the symbols being used, and the correct interpretation of Pi and Theta must be the obvious one, namely, that these letters stand for the two main divisions of ancient philosophy as distinguished by Aristotleand his successors, Practical and Theoretical Theoretical.

— Henry Chadwick: "Theta On Philosophy's Dress In Boethius", Medium Ævum, 1980, Vol. 49, No. 2 (1980), pp.175–179. jstor

So, why stop there?

In his writings, Zosimus also represents the planet Mars by an arrow with a point and the letter theta (Θ), for thouras ("the rushing one"). He sometimes adds a pi (Π) as an abbreviation for the epithet pyroeis ("the fiery one"). […]

The letter theta (Θ) was, in its archaic form, written as a cross within a circle (⊕, ⊗), and later as a line or point within a circle (⊝, ⊙). According to Porphyry (232–305 C.E.) , the Egyptians used an X within a circle as a symbol of the soul. Having a value of nine, it was used as a symbol for the Ennead, the nine major deities of the ancient Egyptians. The earliest of these, the Great Ennead of Heliopolis, was comprised of the original creator god, Atum (often identified with Ra); his children, Shu and Tefnut; their children, Geb and Nut; and the fourth generation, the brothers, Osiris and Seth, and their sisters, Isis and Nephthys. […]

Similarly, the letter Μ appears frequently as an abbreviation for Mary (Maria), theta (Θ) is the initial used for God (theos); upsilon (Y) for the Son ([h]uios); and pi (Π) as the initial of the Father [pater). […]

While most of these voces magicae seem to be nonsense-words, some show traces of their derivation. That associated with theta, for instance, (THOTHOUTHOTH), contains a triple repetition of the name of the god Thouth or Thoth, the ibis-headed Egyptian god whom the Greeks called "thrice-greatest Hermes." […]

Moreover, the Tetrad, explaining these things to him more fully, said:- I wish now to show thee Truth [Aletheia] herself; for I have brought her down from the dwellings above, that thou mayest see her without a veil, and understand her beauty—that thou mayest also hear her speaking, and admire her wisdom. Behold then, her head on high, Alpha and Omega, her neck, Beta and Psi; her shoulders with her hands, Gamma and Chi, her breast, Delta and Phi, her diaphragm, Epsilon and Upsilon, her back, Zeta and Tau, her belly, Eta and Sigma, her thighs, Theta and Rho, her knees, Iota and Pi; her legs, Kappa and Omicron, her ankles, Lambda and Xi; her feet Mu and Nu. Such is the body of Truth, according to this magician, such the figure of the element, such the character of the letter… […]

The "first and the perfect terminus of number" is 9, which completes the first Pythagorean decad. It is called "perfect" because it is the square of three and is represented by the letter theta (Θ).

— Kieran Barry: "The Greek Qabalah. Alphabetic Mysticism and Numerology in the Ancient World", Samuel Weiser: York Beach, 1999.

That within any early Christian context the symbol for death also means 'new life' —after death/resurrection— should be self-evident. The pure cross is just the same in that regard. But since since the association with unlucky/death seems to be the much more prominent one, let's spell that out as well for a less ‘projected’ meaning, but for the practical evidence, with the emphasis on theta being used as an acronym for not for Thanatos (death) but for Theos (God):

“Christ” was often abbreviated with the Christogram ☧, chi-rho. “God,” Θεός, for its part, was sometimes abbreviated with the simple theta, and Jesus was already simply called “God” in the New Testament (John 1:1–18) and in the works of the apostolic fathers (see, e.g., Ignatius, To the Romans, salutation).

— Tuomas Rasimus: "Revisiting the Ichthys: A Suggestion Concerning the Origins of Christological Fish Symbolism", in: Christian H. Bull, Liv Ingeborg Lied & John D. Turner (eds): "Mystery and Secrecy in the Nag Hammadi Collection and Other Ancient Literature: Ideas and Practices. Studies for Einar Thomassen at Sixty", Nag Hammadi and Manichaean Studies 76, Brill: Leiden, Boston, 2012.

The font of all that is true knowledge (Wikipedia) states:

In ancient times, Tau was used as a symbol for life or resurrection, whereas the eighth letter of the Greek alphabet, theta, was considered the symbol of death.: