What is the purpose of a 'Squib' kick in American Football?
Basically the squib kick is used at the end of the half or end of the game to run out the clock, and keep the ball away from a top of the line return guy. You basically pooch it down the field so someone bigger has to pick it up and run with it, instead of putting it in the hands of the other teams return specialist.
According to Wikipedia:
The Squib kick is a tactic used to prevent a long return, usually at the end of the half. On average the receiving team will gain better field position than it would returning a normal kick. However it is considered worthwhile by the kicking team, as it is more difficult to return for a touchdown. Also it must be returned, which isn't the case on a touchback, and thus it takes time off the clock and often brings the half to an end.
Here is an actual example of a squib kick so people get the gist of what the procedure is, and why it happens.
It is also very common to try a squib kick when a team has a particularly good returner. In a kickoff, the man back (sometimes 2 guys) are quick folks, but the guys in front of them are a slower (outside linebackers or even offensive linemen) as their intent is to block, not return the ball. By performing a squib kick, you can almost force the slower group of blockers to pick up the ball and run, hence you nullify the threat of the good returner running for a long return and getting his team good field position
I have also seen the squib used (especially in lower levels) as a sort of hybrid onside/regular kickoff. Pooching the ball between the front line and return men can force someone not used to handling the ball into a position to make a play or let the ball roll by them. Forcing the other team into this non routine play can be beneficial to the kicking team.
In general, however it seems like many times they are a mistake that sets up the receiving team for game tying or game winning field goals at a higher percentage than giving up a return touchdown after a traditional kickoff.