Since nobody has mentioned this yet, let me add one other important point to the great answers already given (ie: that since it was from top to bottom, it shows it was God doing the ripping -@Waggers, that it meant God was opening His holiness to all men through Jesus -@Jonathon Byrd).
With the tearing of the curtain, the atonement ritual for Yom Kippur (the day of atonement) could no longer be performed.
Therefore, ever since that very moment, the Jews have not been able to perform the yearly atonement ritual required by God under the Mosaic pact (especially since the temple was destroyed by the Romans in the year 70 AD). In other words, they no longer have any God-approved means of having their sins atoned for under the Mosaic pact.
By physically removing the ability to perform the atonement ritual and sacrifice, God sent the message that "it is done", and that:
- as He promised in Isaiah, the Messiah atoned for our sins, and
- as He promised Abraham, He provided the sacrifice.
Jeremiah 31:31 tells us that God promised He would establish a new pact with Israel. This new pact supersedes the Mosaic pact (which can no longer provide atonement for sins) and is a pact in Jesus' blood (Matthew 26:28). The tearing of the curtain also gives the picture of a contract being ripped in half. The old pact is literally torn in half, and the new one is now in effect.