It's a sort of exercise where you hold yourself in a position as though you're going to do a push up, so supporting your body weight on your feet and either hands or your forearms while suspending your body a few inches off the floor. The aim is to just hold this position for as long as you can, normally.

See: https://en.wikipedia.org/wiki/Plank_(exercise)

Good core exercise, probably inappropriate for meetings.

The plank exercise is very similar to a pushup exercise move. It comes from making your body straight as a board (plank of wood). The position is face-down on the ground, with all of your weight supported by your toes and forearms.

It is generally difficult to hold that position in proper form for long periods of time (or at least your muscles start to ache)