To jaywalk is to cross the street in an illegal or unsafe manner.
Illegal. Most often this means crossing the street in the middle (as opposed to at the corner), or to cross against the traffic signal. The word is often used in this sense in the USA.
Unsafe. To cross the road slowly, or without paying attention to traffic. This is apparently common usage in most countries aside from the USA.
This word was apparently coined in Boston, MA sometime around 1917. The local paper, The Bostonian, wanted a simple way of saying 'crossing the against traffic signals,' and so the word was born. Weather or not it was actually The Bostonian that coined the term, the 'Jay,' almost certainly comes from the slang term for a stupid or foolish person.
Often written jay walk, but all the dictionaries I've checked agree that there should not be a space.