What is meant by escape from all signs?

There's some other discussion of it here (with lots of references): Understanding animittā (signlessness) as in AN6.13

I think that "sign" i.e. nimitta is a vague or general-purpose word, like the English word "attribute" or "aspect" or "characteristic" -- when I say that word is vague or unclear I mean because different things have different characteristics (different appearances) -- perhaps I should call it an abstract word, if it's one word that describes character or whatever it is that all (different) characteristics have in common.

As well as being used to describe sense-objects, the word ("sign" or "nimitta") is often used (or is more frequently used, in Buddhist talk) to describe meditation stages or "attainments" (e.g. here or here).

Volume 19 of Piya Tan's Sutta Discovery series consists of topics related to "Nimitta".

SD 19.7 starts with different definitions of Nimitta ("object", "basis", "condition"), and how the word is used in the context of meditation.

But his paper which describes "signless concentration" is later, i.e. it's an element of volume 24 which describes "mental concentration (samadhi)" -- see The Discourse on the Question of the Signless Concentration of Mind which begins with,

The term, “signless concentration of mind” (animitta ceto,samādhi) is not fully explained in the Nikāyas, “but its placement after the eighth formless attainment [of S 40.9] suggests it is a samādhi qualitatively different from those attained in samatha meditation.”

I think it's related to the topic in SD 19.14 -- "Theme: Sense-restraint & wise attention: how to master the senses". A lot (but not all) of that is Abhidhamma material -- its topic is the formula which appears in several suttas:

Here, bhikshus, when a monk sees a form with the eye, he grasps neither its sign nor its details.

In that context I think that a sign is your first impression of something, and its details are what you discern afterwards if you then focus on that thing.

When you get a first impression of something the (unmindful or "unreleased") consciousness will "follow" the sign.

According to Mahayana interpretation, "signs" or "marks" are concepts, or conceptual designations, also known as preconceptions.

The problem with conceptual designations is that we tend to confuse them with reality (=to reify; noun "reification"). To give a canonical example, when someone is attached to his own personal stereotype of what an "attractive woman" should look like, when he meets one that matches his stereotype he no longer sees her as a complete person, instead he only sees his own concept of woman, he sees a sexual object! Then we tend to look with our conceptual brain, instead of looking with an open mind. Then, all we see is our preconceptions or biases - instead of seeing what actually is. Not only we see nothing but our preconceptions, we completely confuse them for reality, we think that what we "think" is what really "is" - but it is not, we see our own mental fabrication! Then on the basis of that fabrication, we develop certain attitude toward the object - for example we want to make acquaintance with the woman, with an implicit intent to get close with her. This is called "following the drift of signs".

Another example of this is racial stereotyping. You see a person of a national origin that you generally associate with ignorant violence - and then all you see is your preconception, you no longer see the real person. On the basis of this you develop aversion to this person, which ends up causing a conflict.

This happens with inanimate objects as well. Once we know that a given object is "a tree" - we no longer really see it as-is, we see our concept: "a tree". It takes a special effort to unsee our abstract concept and see the actual tree.

According to Mahayana, the entire Samsara is an illusory world completely made of such concepts! The notion of "I" or atman is one of such preconceptions. It is on the basis of attachment to preconceptions that we have unsatisfied craving, which manifests as suffering. Complete cessation of reification is "escape from all signs".

This is a rather simplified presentation, it actually goes much deeper than that, but this can get you started. Entire Mahayana was born from study and development of this teaching, passed in the oral form from Buddha's students to next generations. In Mahayana we refer to this as "shunyata" and "prajna-paramita", but it is also present in the Pali Canon in quite a few places like this one, using terms like "groundless", "having no position", "signless" etc.