Marking and pressing are 2 different things, but they are complementary to each other.
Consider zonal marking, with four zones,1,2,3 and 4 in midfield. Say you have 4 red players (R1, R2, R3 and R4) and 5 blue players(B1, B2, B3, B4, B5). Another player, acting as a neutral player is about to send the ball in the midfield area. R1, R2, R3, R4 and R4 can mark B1, B2, B3, and B4 respectively. The ball is sent to B5. The red players have two options, either to keep on marking the other blue players as they did earlier, or one or several of them leaves his marking duties and go to press B5, so that possession may be recovered quickly. Or, he can let B5 come and try to pass to another blue player in his zone that he is marking.
Suppose that all red players allow B5 to operate freely with the ball. B5 enters the zone of R4, then R4 may press him to try to force an error or steal the ball from him. B4 will be free to receive the ball. Or R4 may keep on marking B4 and allow B5 to keep on progressing alone.
The idea of using a 3 man pressing system on a player is to force the player to give back possession (make errors, rush in passing, and so on). This allows little room for the player to operate. Doing this requires a lot of physical condition.