There are variations, but in its simplest form it consists of taking a problem and asking Why , invariably the answer will prompt another Why and so on. Typically 5 Whys will get to the root of the problem, which initially may not be obvious.
For example
A review of breakdowns (in a CMMS) on a shoulder pin identified that a pin is now failing regularly but that it ran for many years without a problem.
1 - Why does it fail – it shears and breaks
2 - Why does it shear – because of excessive loading
3 - Why is there excessive loading on the pin – because the adjoining part was redesigned to get more output from the machine and this increases the load on the pin
4 - Why didn't this part get upgraded – because it was not identified as a potential problem
5 - Why was it not identified as a potential problem – because we don't have a formalized Modification Procedure which would have identified the impact of upgrading the adjoining part

In this particular case, lack of a “Modification Procedure” is the root cause,  though without the 5 Whys, this may not have been the obvious conclusion.

 Read - Computer Maintenance Management System: Capture the Data – Close the Loop