The key difference between require() and include() is that if you require() a file that can't be loaded (e.g. if it isn't there) then it generates a fatal error which will halt the execution of the page completely, and no more output will be generated. On the other hand, if you include() a file that can't be loaded, then this will merely generate a warning and continue building the page.
require will produce a fatal error (
E_COMPILE_ERROR) and stop the script
include will only produce a warning (
E_WARNING) and the script will continue