string theory - What exactly does it mean to wrap a D-brane or a M-brane in a Riemann surface $Sigma_g$?

What exactly does it mean to wrap a D-brane or an M-brane in a Riemann surface $\Sigma_g$ ($g$ is the genous)? Is there some mathematical statement? And why do we get various supersymmetric gauge theories out of this?

Is there any relation to compactifications? Is there a good place for a read on the "wrapping" of branes on Riemann surfaces?

P.S. As far as the references are concerned I would appreciate something "easier" than Nunez's and Maldacena's paper for example (http://arxiv.org/abs/hep-th/0007018). Thanks!