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:
John 2:18
The Jews then said to Him, “ What sign do You show us as your authority for doing these things?” (italics added)
John 2:23
Now when He was in Jerusalem at the Passover, during the feast, many believed in His name, observing His signs which He was doing. (italics added)
John 3:2
this man came to Jesus by night and said to Him, “ Rabbi, we know that You have come from God as a teacher; for no one can do these signs that You do unless God is with him.” (italics added)
John 4:48
So Jesus said to him, “Unless you people see signs and wonders, you simply will not believe.”
John 6:14
Therefore when the people saw the sign which He had performed, they said, “This is truly the Prophet who is to come into the world.” (italics added)
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.]