What is the meaning of 相声?
相声 is a form of Chinese traditional stand-up comedy where two two performers talk back and forth to each other, telling a funny story or just chatting about a humorous topic. Because it's a traditional Chinese art form and originates in northern China, it has a higher political status than other Chinese art forms. This means that it gets broadcasted across the country on CCTV a lot, and sinophiles like Mark Roswell get introduced to it when they are studying Chinese. 

相声 performers who become make a name for themselves can establish their own styles and take on students to pass on their skills. Mr Roswell/Dashan's mentor was a performer named  姜昆. Dashan is not the only foreigner to have studied under a famous artist -- another name that I remember off the top of my head is Julien Gaudfroy (朱力安), a French student of Chinese who also studied 相声.

Probably the best way to get a better feel for 相声 would be to search for the term on Youtube, or if you're in China then search on Youku. Combine it with 大山 or 朱力安 to find videos of these talented performers.