I've tried to locate this particular sound in a drum kit, but I can't figure out what it's called. It's equivalent to hitting your drumsticks together on every second and fourth beat of a song during the verse or pre-chorus. Usually the kick bass is played on the first and third beats. But the clicking sound usually transitions into a full on snare in the chorus of the song. Here's an example of this.

As you'll notice, towards the pre-chorus of this song, even though it was probably done using beatboxing, the clicking is still there, on the second and fourth beats of the piece.