It's compiler dependent. That said, in general using " prioritizes headers in the current working directory over system headers. <> usually is used for system headers. From to the specification (Section 6.10.2):
A preprocessing directive of the form
# include <h-char-sequence> new-line
searches a sequence of implementation-defined places for a header identified uniquely by the specified sequence between the < and > delimiters, and causes the replacement of that directive by the entire contents of the header. How the places are specified or the header identified is implementation-defined.
A preprocessing directive of the form
# include "q-char-sequence" new-line
causes the replacement of that directive by the entire contents of the source file identified by the specified sequence between the " delimiters. The named source file is searched for in an implementation-defined manner. If this search is not supported, or if the search fails, the directive is reprocessed as if it read
# include <h-char-sequence> new-line
with the identical contained sequence (including > characters, if any) from the original
directive.
So on most compilers, using the "" first checks your local directory, and if it doesn't find a match then moves on to check the system paths. Using <> starts the search with system headers.