Comparison Functor Types vs. operator<

In the Google C++ Style Guide, the section on Operator Overloading recommends against overloading any operators ("except in rare, special circumstances"). Specifically, it recommends:

In particular, do not overload operator== or operator< just so that your class can be used as a key in an STL container; instead, you should create equality and comparison functor types when declaring the container.

I'm a little fuzzy on what such a functor would look like, but my main question is, why would you want to write your own functors for this? Wouldn't defining operator<, and using the standard std::less<T> function, be simpler? Is there any advantage to using one over the other?