It means that this function does not modify the observable state of an object.
In compiler terms, it means that you cannot call a function on a const object (or const reference or const pointer) unless that function is also declared to be const. Also, methods which are declared const are not allowed to call methods which are not.
Update: as Aasmund totally correctly adds, const methods are allowed to change the value of members declared to be mutable.
For example, it might make sense to have a read-only operation (e.g. int CalculateSomeValue() const) which caches its results because it's expensive to call. In this case, you need to have a mutable member to write the cached results to.
I apologize for the omission, I was trying to be fast and to the point. :)