It affects where the preprocessor searches for the include file. From MSDN:
"Quoted form: This form instructs the preprocessor to look for include files in the same directory of the file that contains the #include statement, and then in the directories of any files that include (#include) that file. The preprocessor then searches along the path specified by the /I compiler option, then along paths specified by the INCLUDE environment variable.
Angle-bracket form: This form instructs the preprocessor to search for include files first along the path specified by the /I compiler option, then, when compiling from the command line, along the path specified by the INCLUDE environment variable."
As a rough guide, I only use quotes when I'm trying to specify a path relative to the directory containing the file with the #include in it. Otherwise, I just use angle brackets. As an example from my current project:
#include // standard library headers
#include
#include
#include // third-party library headers
#include
#include // specified relative to my own base include dir
#include "PartitionForest.h" // a header in the current directory
