An Urca process is a reaction by which a neutrino is emitted from a baryon. It is thought to be a means by which energy is emitted from white dwarves and neutron stars. This can happen in a number of ways, typically a baryon (e.g., mass number) either absorbing or emitting a lepton (e.g., electron), but also emitting a neutrino during the reaction. The end result is faster cooling.
Regarding capitalization of Urca, the original theorists, Gamow and Schoenberg, first spelled it urca process in their 1941 paper. It is now sometimes written as the Urca process and sometimes URCA process. The name was apparently inspired by the Urca Casino in the Urca neighborhood of Rio de Janeiro where early discussions took place.