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

It depends on when you do a burn-in test. If you do it as soon as you build a new computer, then backups are not necessary, since you didn't put anything on there worth saving yet. But the reason you should do backups would be if you ran such a test on a computer which has valuable data on it. Such testing can push the hardware over the edge, and then you won't have access to your data.