What is that?
It's a multi-function device that Leela specifically referred to as her Wristlojackimator in the episode "How Hermes Requisitioned His Groove Back". All other mentions she makes of it are general and vague (i.e. "this thing I wear on my wrist" or "my wrist thingy").
The functions/abilities of her "wrist thingy" are:
In addition, as NominSim mentions in a comment, Leela keeps the bracelet she was found with as a child underneath it ("Leela's Homeworld").