Wikipedia's entry for crossbar is diluted with discussions of
fusible link EPROMs and old telco mechanical switches. A better place
to go is Greg Ferro's blog. He gave a straight-forward
definition of a crossbar in August 2011. Greg has a follow-on blog
entry on Buffers for a Switch Fabric written in Sept 2011.
What should be the next blog entry in Ferro's series is details about how crossbars can be equipped with fancy arbitors to facilitate switching even when the packet at the head of the line needs to be buffered. For example, setting up queues per output port in each input buffer and then permitting packets to cross the fabric when they can find an open path can help with head-of-line blocking. So can arbitors that can reach into the middle of a queue to search for a packet that isn't blocked.
Rich Seifert's The Switch Book  discusses these techniques. Seifert produced a second edition All-New Switch Book in 2008 but the material on crossbar switching has not been substantially changed.