The Tiller is used to steer the aircraft on the ground. It normally turns the nosewheel and the rest of the aircraft follows in sympathy.
In the 737 it's a triangular segment (shaped like slice of pizza), with a gap for the fingers to slide into.
There's always one on the left hand side, just forward and left of the Captain's knee.
Optionally one can also be fitted on the right hand side.