#include <foo.h> searches the libraries folder, along with a few other folders.
#include "foo.h" searches the local folder, then the rest of the include path (the libraries folder and others). But you need to understand that "local" is relative to the file that contains the #include directive. So if you have this:
{Sketchbook folder}
|_MySketch
| |_MySketch.ino
| |_Robot.h
|_libraries
|_MyLibrary
|_MyLibrary.h
and MyLibrary.h contains the line:
#include "Robot.h"
Then Robot.h will not be found because in this context "local" meant the MyLibrary folder, not the MySketch folder.