Why was there a 'governor' at the Wedding in Cana?

From the McClintock and Strong Biblical Cyclopedia, entry Architriclinus (bold emphasis is mine):

Architriclinus (Α᾿ρχιτρίκλινος, master of the triclinium or dinner-bed, SEE ACCUBATION), rendered in Joh 2:8-9, "governor of the feast" (q.v.), equivalent to the Roman Magister Convivii. The Greeks also denoted the same social office by the title of Symposiarch (συμποσίαρχος). He was not the giver of the feast, but one of the guests specially chosen to direct the entertainment, and promote harmony and good fellowship among the company. (See Potter's Gr. Ant. 2, 386.) In the apocryphal Ecclesiasticus (35:1, 2) the duties of this officer among the Jews are indicated. He is there, however, called ἡγούμενος: "If thou be made the master [of a feast], lift not thyself up, but be among them as one of the rest; take diligent care for them, and so sit down; and when thou hast done all thy office, take thy place, that thou mayest be merry with them, and receive a crown for thy well ordering of the feast." (See Walch, De Architriclinio, Jen. 1753; Brendel, De loco Joh. Eisenb. 1785.) SEE BANQUET.

To answer a question about why John reports that there was an arcitriklinw--the actual Greek word used--at the Wedding in Cana, the best answer is that John thought it necessary to eliminate future questions about the quality of the wine resulting form Our Lord's miracle.

While John's narrative was about a Jewish wedding, the language in which John wrote the narrative, and that the readers for whom he wrote it understood, was Greek, so it is natural for John the Gospeler to adopt a Greek name for a functionary of the wedding, even if the Parable is about a Hebrew wedding.

As to what the complete role and function of the person identified by the Greek word used by John, there is little agreement among translators from the Greek what this actually meant. According to this website, The KJV, and Noah Webster's translation render the word as "governor", but other translators use the terms "ruler of the feast", "master of the feast", "feast master", "chief steward", "President", and "director of the apartment". Beyond rendering a judgement of the quality of the wine resulting from Jesus' actions, it is not clear what else the arcitriklinw might have been responsible for, and it is really not relevant to John's narrative.

The Apocrypha will help on this issue. Sirach, which is believed to have had a Hebrew original (e.g. DSS) and which is quoted several times in Hebrew in the Talmud, has a chapter concerning being the master of a feast:

Sirach 32:1-9 (NRSV)

If they make you master of the feast, do not exalt yourself; be among them as one of their number. Take care of them first and then sit down; 2 when you have fulfilled all your duties, take your place, so that you may be merry along with them and receive a wreath for your excellent leadership.

3 Speak, you who are older, for it is your right, but with accurate knowledge, and do not interrupt the music. 4 Where there is entertainment, do not pour out talk; do not display your cleverness at the wrong time.

... 9 Among the great do not act as their equal; and when another is speaking, do not babble.

Greek of the first verse of Sirach 32 (from ellopos):

῾Ηγούμενόν σε κατέστησαν; μὴ ἐπαίρου· γίνου ἐν αὐτοῖς ὡς εἷς ἐξ αὐτῶν, φρόντισον αὐτῶν καὶ οὕτω κάθισον.

The word just refers to a governor and is not specific to ruling feasts. NRSV obviously added the words "of the feast" from a consideration of the context. This is confirmed by looking at the KJV, which has "If thou be made the master of a feast, lift not thyself up..." (italics theirs)

Versus the Greek of John 2:9 (using the Greek Orthodox Patriarchal Text):

ὡς δὲ ἐγεύσατο ὁ ἀρχιτρίκλινος τὸ ὕδωρ οἶνον γεγενημένον—καὶ οὐκ ᾔδει πόθεν ἐστίν· οἱ δὲ διάκονοι ᾔδεισαν οἱ ἠντληκότες τὸ ὕδωρ—φωνεῖ τὸν νυμφίον ὁ ἀρχιτρίκλινος