To leave all of your friends and acquaintances behind; to cause permanent damage in your relationships.

1) Even though you're quitting your job tomorrow, try not to burn your bridges. You never know when you'll need help in the future.
2) There may be a conflict of interest if I work with both companies. Of course I don't want to burn any bridges, so I should choose one company and let the other know that I can't work with them.

Etymology: People form bridges to their past. If you forget or insult your relationships, you burn your bridges and cannot go back. (How true!)