Question

Why is it important to back up data on a computer before you burn-in test the cpu?

Answer 1

A burn-in test is a test which is usually performed on a system or component by running it for a long time in order to bring out any errors or system failures etc. 
While doing it on CPU the data must be backed up as any kind of error or failure may result in the loss of data, at time systems can be repaired to retrieve data but still there is no guarantee, backing up is the best option.