Desempeñar is an interesting verb brought to us courtesy of our Nicaraguan friends Leonido and Doña Coco. It basically means "to do" but goes a little further than that.
¿Qué trabajo desempeña aquí?
"What work do you carry out here?"
[Caption 1, Doña Coco > La Vida De Una Cocinera]
Desempeñar implies a time progression, a job or role that is being done or carried out. "Desempeñarse como secretaria would be "To hold a secretary position," and Miguel desempeña un papel importante en el proyecto is "Miguel plays an important part in the project."
Further, the word desempeñar points to obligations and responsibilities related to the role or job being accomplished. After all, desempeño is translated as "performance" and when you’re doing something con empeño (with diligence / with earnestness), it means that you’re putting great care and heart into it.
But beware! These words are used in another sense as well: Empeñar is "to pawn" which makes desempeñar the action of going to the pawnshop and getting back all your jewelry (to redeem it).
Sidenote: Yabla Spanish subscribers should go back and check out caption 8 of the song El Apostador by the band Control Machete, 'Casa voy a empeñar' --House I'm going to pawn.]