To be "notorious" means that you are famous or well-known for doing something bad. For example:

Blackbeard was a notorious pirate who raided ships in the early 18th century off the east coast of the United States.

The word "notorious" doesn't quite fit with the idea of someone who forgets birthdays, like in the example above. But people sometimes call themselves or other people "notorious" as an exaggeration. It's said as kind of joke.

To describe the bad things that a person does that make them notorious, you say that they "are notorious for ___":

Arnold is notorious for yelling at employees and throwing things around when he gets in a bad mood.