This has more to do with C and C++ than Unix, and as such belongs to SO.
To answer your question, the
<> indicates headers in the standard library and
"" the libraries written specifically for the project.
From the K&R:
Any source line of the form
is replaced by the contents of the file filename. If the filename is quoted, searching for the file typically begins where the source program was found; if it is not found there, or if the name is enclosed in < and >, searching follows an implementation-defined rule to find the file. An included file may itself contain #include lines