What is "Playing For Top or Bottom" In Bridge?
This answer is specific to Matchpoints. In Matchpoints, playing for top or bottom means that if you succeed, you get a top, otherwise you get a bottom. (Note: I haven't heard of people talking about top/bottom in other forms of duplicate).

Any play could potentially be called this way, including safety plays.

To give a specific example of where a safety play might be considered playing for top or bottom, consider the following hand:

♠: AT8xx
♡: AKx
♢: AKx
♣: Kx

♠: K97x
♡: Qxx
♢: Qxx
♣: Axx


You are playing matchpoints and have reached the contract of 6♠. You also think that the rest of players in your direction will do the same. Say you get a club lead.

Now if this were rubber bridge, you could almost ensure 12 tricks by winning the club K and playing a low spade towards the 7. If RHO follows, you play the 7. If RHO shows out, you win the K and play toward the AT. LHO can only get one spade trick (barring really bad breaks in other suits).

Basically, ducking the first round of spades is a safety play to cater to QJxx spades with one of the opponents.

At Matchpoints, however, the normal play is to bang down the AK, making 13 tricks if trumps are 2-2 and still have chances for making 13 if they are 3-1 with a singleton Q or J.

Assuming the field will not take the safety play, by taking the safety play ("going against the field"), you get a top if QJxx is held by one opponent (and rest of the field goes down by guessing to cash the honour in the wrong hand first). You will get a bottom if trumps are 2-2, or there is a singleton Q or J (you make exactly 12 tricks, while the rest make 13).

We ignore QJx, as we expect opponents to split QJ and ensure a trick. You get an average in that case (everyone makes exactly 12 tricks).