It's a question terminated employees who are considering litigation against a former employer ask of employment lawyer. So what exactly is this strange thing, “mitigation of damages”?
In short, it means that if you want to have a chance to collect the most money possible by seeking “front pay,” you can't sit on your tail eating bon bons all day while waiting for the lawsuit to solve your financial problems. You must actively look for a job. If you don't the courts will deem you to have withdrawn from the workforce. And if you're not in the workforce, you have no legitimate expectation of getting paid for the time you were out of the workforce.
Molly DiBianca of the Delaware Employment Law Blog has a good post on this subject, which goes into more detail. As Molly correctly points out, application of the duty to mitigate in the real world is not always a black or white proposition. But the essential concept is settled: make no effort to find work and you will not be eligible for an award of front pay.
Therefore, as a terminated employee, it is important to keep complete and accurate records of all of your job search efforts. It's not enough to say that you were looking. You have to be able to prove it.