Hooks are functions you write, which get called by core or other modules to modify how things are processed and output.
For example, to modify a form, you would use HOOK_form_alter($form, &$form_state, $form_id).
Replace HOOK with the machine name of your module and clear the cache to activate it.
Code within this function can modify forms as they are loaded and displayed.
Modules document hooks in MODULE.api.php files. Look for these to read up on ways to modify module functions.