A computer program is made up of lots of computer instructions (millions of them).
These instructions EXECUTE one after the other.
Sometimes one instruction will go wrong for some reason and may crash or "kill" the program (a FATAL instruction).
So a fatal execution error is where one computer instruction has failed so badly it has killed the program.
If you are going to ask WHY this happens it is impossible to say without knowing the program, any messages you got, and so on.
It may be software related, hardware related, or just a certain set of circumstances that caused the error.
It may never happen again, or it may happen each time you run the program, difficult to say.