What does this mean (functions)

The backslash '\' means 'not including'.

So your thing basically says that 'f' is a function mapping from the set of real numbers (not including -1) to the set of real numbers (not including 1).

EDIT: For example, if you had a set X = {0,1,2,3,4,5}. Then the set X \ {2} would be the set {0,1,3,4,5}.