Yeshu'a did this beginning of the signs in Kana of Galil, and he manifested his glory, and his disciples believed in him. (John 2:11)
What were these "signs" a sign/ indication of?
Simply put the 'signs' of Christ were those miracles that manifested his divinity. They were 'pointers' to his divinity and nature of ministry acting as sign posts of authority and seals of divinity. The miracle, or sign, of changing water into wine was the first of his ministry of which there were many afterwards. His signs manifested not just the divinity but the glory of his person and ministry as meek, mild, compassionate, empathetic healer and savior who sanctified and restored all of life as a humble servant and Son of Man on a cross.
This is quite unlike most miracles in the Old Testament which were often a miraculous destruction of sinners. This was 'new wine' in a new covenant that promised better things. Right from the outset Jesus seems much different from John the Baptists, the last of the Old Testament prophets, for John, on his peculiar ministry would not even drink wine and it does not seem like his ministry would tolerate any eating or drinking at a wedding.
This 'sign' which manifested his unique glory, divinity and humble purpose was striking and naturally believed by his true disciples. It was entirely consistent with everything the gospel proclaims - God's manifested kindness and grace in Christ.
Miracles are the ”works” the Father gives to the Son to do, to provide proof that His teachings, ”words” are true. The miracles convince the disciples that Jesus is to be believed. Nicodemus is clear that no one could do the works Jesus did unless the Father was with him.
Look at soldarnal's answer at Who does Jesus refer to by the phrase “another who testifies about me” in John 5:32?
This should give us food for thought here:
Although I heartily agree with the spirit of the answers already given, I think it is important to explore what John himself had in mind when he penned the words in question. When you take a look at some of the other usages of "sign" in John's gospel (and there are several), a pattern emerges. Here is a sampling:
That final reference is probably the clearest. The signs were intended to confirm Jesus' identity as the Messianic Prophet, sent by God, as foretold in Deut 18 and elsewhere. (This perhaps echoes the idea found in Deut 13:1 that prophets are confirmed by both signs/wonders AND a Biblical message.)
[Note: That the people (or even the disciples) understood that He was, in fact, God incarnate is less certain. His divine identity unfolds gradually for most observers in John's gospel. Consider Thomas for example - Jn 20:28.]