It means that she was a little depressed, or just not her usual self (for example: a person who is very good at school forgetting to study and failing for a text the next day....or a good football player like Messi playing badly....he was just not feeling like himself that day.

It is a little less serious, and more general than 'feeling ill'. It could mean she was a little ill or unwell. It could also mean she was a little depressed, or just was tired and lacking sleep. It could even be a euphemism for saying that she was having her period. It is a nice way of saying she wasn't as capable as she normally would be, without being rude, and giving details.

It doesn't necessarily imply that she was ill, all it means it that she wasn't feeling the way she usually felt. This could be physically or mentally/psychologically. Another expression for this is "out of sorts", as in "She was feeling a little out of sorts that day".

I think your sentence is missing a word: She was not feeling like herself ... This sentence simply means she is acting or feeling in a way she doesn't normally act. In your example: if the girl never forgets any thing and is never late, and suddenly one day, she forgets everything and is late, then you would say ... Wow. Susan is not like or (is not feeling like) herself today. So the next day, when Susan is now feeling or acting normal, you can say, "Susan is like her old self."