As the other answers explain, for a std::map you can use find.
To answer the question in the headline:
For iterators, const can refer to the iterator itself, or the to the contents, the iterator points to. Both properties are orthogonal. With STL notation you have the following cases:
iterator Contents and iterator can be modified.
const_iterator Contents is const, the iterator can be modified
const iterator Contents can be modified, the iterator is const.
const const_iterator Contents and iterator are constant.
It is similar for pointers. There, the const can also refer to the contents or the pointer itself.