Re-raising the raiser shows even more strength, and it is often the beginning of the slippery slope towards stacking off, or doubling up (with 100bb stacks).
There are some typical 3-bet situations that develop, so let's take a look at them.
♠ Big Hands
This one is obvious. If the mantra is to get it all in before the flop with AA or KK (100bb stacks or less), then obviously you're re-raising when you look down and see Rockets or Cowboys in the hole.
♠ Out of the Blinds against a Steal
The first creative use of the 3-bet. If a player is stealing from the blinds too often, he can't be doing it with premium holdings every time. So, some players will reraise out of the blinds with hands that they wouldn't usually reraise with, knowing that there's a chance that the stealer probably doesn't have a hand strong enough to stand up to their reraise.
Of course, the player in the blinds might have a monstor. It doesn't matter. This situation is a common place to find players 3-betting, usually in an attempt to stun (or take advantage of) constant blind stealing aggression.
♠ On The Button
In a move that mimics "punishing the limpers", some players guard the button with a 3-betting fever. This usually takes place when the other players are raising a LOT of hands.
The player on the button will have position for the rest of the hand (should the blinds fold, which is usually the case). So, they have a distinct advantage. And, if the original raiser is raising say, 23% of their hands, there is a good chance that they are raising with hands that won't play well in a re-raised pot, out of position.
In both of these last two instances, the decision to 3-bet is a reaction to a read on the other player's tendancies. Basically, when a player constantly raises hands that should not be raised 100% of the time, someone will "play back" at them. The 3-bet is a weapon used by those who are "playing back". And those two positions at the table, the button and the blinds, are places where you'll see players make use of that weapon.
♠ Isolation
If a particular player is playing poorly, or is perhaps overly aggressive (tilting?), some of the other players may use the 3-bet to isolate him in a hand. By 3-betting instead of simply calling a raise, a player can make it too expensive for others to enter the hand.
♠ The Squeeze
The Squeeze is a "play" that takes place when a player open raises, and gets a cold caller. Now, any players in later position can reraise and put the "squeeze" on the other two.
What's the thinking behind this play?
Some players open raise with a wide range. While the opening raiser may have Aces, it's more likely they have something like AQs, or JJ, or KQs/AJs/TT. When someone simply calls them, they are saying they too have a good hand, but probably not AA/KK quailty. Here enters the player, in position, who can up the ante to uncomfortable levels by raising both of them.
Now, the initial raiser, knowing he'll be out of position for the rest of the hand, has to respect the potential holdings of both the caller, and the "squeezer". That player will usually be forced to fold.
The caller is left with the option of playing a hand that often results in a win or loss of their stack (at least at a typical online cash game table) while out of position. They too are often forced to fold.
Resources
For more on the topic of 3-betting, check out some of these threads/guides on the topic: