Usually, by using quotes you mean that header files are located in relative positions to your project's directory. If you use angle brackets, on the other hand, compiler would expect your header files locations to be standard locations. Such as /usr/include, /usr/local/include or any other default locations for your compiler.
In GCC if you use the -I flag, includes with angle bracket would be searched in the specified locations also.
Example:
$ gcc -Wall -I/path/to/my/library/include myfile.c
So if you have myfile.h in /path/to/my/library/include, you can use #include in myfile.c source.
