A totally unofficial and non-mathematical explanation:
A safety function rated as SIL 1 means - do the job with a standard system, but do it carefully and check a bit more.
SIL 2 means - you need take a few extra precautions but don't go overboard.
For SIL 3 - you need to add some bells and whistles to make sure the function works when required.
If you get SIL4 - go back and re-engineer the process (or change jobs).
A safety function rated as SIL 1 must function as required better than 90 % of the time (probability of failure on demand less than 0.1)
For SIL 2 the system must function as required 99 % of the time or better.
For SIL 3 it must work 99.9 % of the time.
For SIL 4 99.99 % of the time (probability of failure on demand less than 0.0001)
But note that it is the safety FUNCTION that is SIL-rated - not the hardware that is used as a part of the way to make sure that function is performed. You decide on a SIL rating by looking at the expected risk (severity x probability) associated with failure of the equipment being controlled with no protection, look at the risk level you can tolerate, and then decide how to reduce the risk. Risk reduction is then allocated to various systems.