When you specify your own include paths, they take precedence over the implementation's. So, if you put in one of those paths a file named iostream, when you #include <iostream> you'll be including that file, not the implementation's iostream.
If you use quotes instead of angle brackets the compiler will first look for the file in the path relative to the current file. If it can't find it, it will continue looking in the include paths.
In other words, if you expect the file you're looking for to be in an include path then it doesn't make any difference if you use angle brackets or quotes.