Many tournament players use a rule of thumb that once their stack has dipped below 10 times the big blind, their only plays are to move all-in or fold. This is pretty imprecise and often varies on situational factors, but for the moment, it's not a bad rule of thumb; you'll hardly ever make any serious mistakes by using it.
But what happens when you have about 15-20 times the big blind? Suddenly, moving all-in, while possible, may not seem all that appetizing; clearly, the range with which you should just shove tightens up significantly. At the same time, making a standard raise with a strong hand seems silly, and while limping can work out in the right situations, you'll often feel more comfortable leading the action.
With this sort of awkward in-between stack, the best thing that you can do is often to try to three-bet all in. Once another player raises to 3x the big blind (or thereabouts), your reraise all-in is a lot more comfortable, and has the advantage of picking up a larger pot. This play is especially powerful at tables where you have several aggressive and strong opponents; they're likely to often be raising to steal the blinds and antes, so your pushes will often win uncontested. Yes, sometimes they'll have a legitimate hand and knock you out, but in the long run, this play should be massively profitable -- and help keep you from falling into the dangerous short-stacked zone!
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