What is the meaning of walking off the job?

It is when you quit a job without giving any notice. This is a very bad thing to do because it totally burns your bridge with that company and they will never rehire you. If you are thinking of doing it, don't. Give two weeks notice. Sometimes they don't require it, but if you walk away without giving it you will be blackballed and going back won't be an option. 

I actually disagree with Jane on the terminology - though I do agree that it is very bad form to quit your job by walking out instead of giving proper notice.

To my way of thinking, quitting your job (as Jane described) is more properly known as walking OUT on the job.

Walking OFF the job is tantamount to an employee strike.

Walking off the job is usually a group effort; done to force change of some sort. Perhaps employees want better working conditions or more pay; perhaps there are safety issues which make working at that particular company too dangerous - reasons vary.

In short, walking off the job is like telling the company, 'We have a problem. We're leaving and we're not coming back until you do something about it.'