#include is used to include outside libraries in your sketch. This gives the programmer access to a large group of standard C libraries (groups of pre-made functions), and also libraries written especially for Arduino.
The main reference page for AVR C libraries (AVR is a reference to the Atmel chips on which the Arduino is based) is here.
#include, similar to
#define, has no semicolon terminator, and the compiler will yield cryptic error messages if you add one.
LibraryFile.h: when the angle brackets syntax is used, the libraries paths will be searched for the file.
LocalFile.h: When the double quotes syntax is used, the folder of the file using the
#include directive will be searched for the specified file, then the libraries paths if it was not found in the local path. Use this syntax for header files in the sketch’s folder.