There are situations within a basketball game that can cause a fast break or transition possession where there are 3 offensive players against 3 defensive players, similar to the mismatched matchups like 3-on-2 etc. However, 3-on-3 basketball can also refer to half court games that are very popular these days having only 3 players per team instead of the usual 5 that play full court. It is a fun way to play pickup, intramural, or semi-organized basketball without full court fatigue.
Offense in a 3-on-3 situation is similar to a full 5-on-5 scenario with some subtle differences because of the extra room on the court. Using the entire half court will help the offense use the space they have to their advantage creating easy looks both inside and out. Spreading out the defense as much as possible with effective ball movement will allow the offense to function very easily in these types of scenarios and games.
3-on-3 situations put the defense at a disadvantage compared to a full 5-on-5. Without the extra 2 players, more space must be covered and contested by the defense, which causes a different mindset. Forcing the offense to become predictable and to use only one half of the floor as much as possible will create the worst shot each possession. The defense must protect the paint as best as they can forcing outside shots to beat them if all else fails.