The original slow play is the first time that the slow play tactic was used and it is still the most common time you are likely to see a slow play used. The slow play was originally used by a poker player that had a very strong hand and wanted to see if they could milk their opponent for a bit more money and therefore instead of raising they might just call or instead of betting they might check and try to trap their opponents. Slow plays in this sense work very well if you are playing against an aggressive opponent, but they are not as good if you are playing a bunch of rocks that are unlikely to bet unless they have a really good hand.
The term aggressive slow play might sound a little bit like a misnomer and it is in a sense a bit of an oxymoronic term. However, the main point to drive home with the aggressive slow play is that in addition to the same purpose as the original slow play, there are also raises involved after an opponent has bet. In other words, check-raises instead of check-calls characterize a person that is employing the aggressive slow play. This will usually happen on the turn, although a person might be brave enough to wait until the river and hope that their opponent decides to make one more bet that they can raise, but most players are not willing to risk a free river round without getting at least an extra bet into the pot on the turn and making their opponent pay extra to get to the end of the hand.
Because poker is all about bluffing, it was only a matter of time before the bluffers figured out a way to enter the slow play tactic into their arsenal of different ways to bluff. When you consider a slow play bluff, the one thing that you absolutely need to have without fail is a skilled opponent. A slow play bluff is such an elegant and high class tactic that it will be completely lost on a novice opponent. Novice opponents are not observant enough to think that you might have a good hand when you slow play; they are only considering their hand. A good opponent however, one that is willing to lay hands down, might think twice about betting when you check if it looks like you are slow playing a hand. This can allow you to then bluff on the next street and take the pot down or quite possibly even check your way to the river and see two extra cards for absolutely no extra bets; both of which are pretty sweet possibilities.