What is trapping when you play soccer?

Answer 1

the ball dropping near you so that you can dribble or pass it if you want to

Answer 2

When the ball is coming to you, you must 'trap' it, which is craddling the ball to get it under control under your foot

. The most common is when one receives a pass (someone from your team kicks the ball to you so that it's easy to control), they trap the ball with the instep of the foot which usually happens to be perpendicular to the motion of the ball (since it's easiest).