1. Notices: These are trivial, non-critical errors that PHP encounters while executing a script - for example, accessing a variable that has not yet been defined. By default, such errors are not displayed to the user at all - although, as you will see, you can change this default behaviour.
2. Warnings: These are more serious errors - for example, attempting to include() a file which does not exist. By default, these errors are displayed to the user, but they do not result in script termination.
3. Fatal errors: These are critical errors - for example, instantiating an object of a non-existent class, or calling a non-existent function. These errors cause the immediate termination of the script, and PHP's default behaviour is to display them to the user when they take place.