When your job is "on the line," it is in jeopardy. The job could be saved, but is in danger of being lost. That is, you might be fired if you do not do your job properly. Ex.: "Matt's job was on the line due to his anti-social behavior. If he knew how to work in a team, his job would be secure."
Other things can be on the line, too: your marriage, your future, even your life. Anything "on the line" is in a crisis and could go in either direction (that is, up or down).