Zuko’s mom is Ursa. In Avatar: The Last Airbender , she disappears from his life, and the full story is revealed later in the comic The Search : she helped Ozai by making a poison that killed Fire Lord Azulon, and in return Ozai forced her to leave the Fire Nation and cut ties with her children.

What happened to her

Ursa went back to her hometown of Hira’a and later changed both her appearance and memories with the help of a spirit called the Mother of Faces, so she could live a new life away from Ozai. That’s why Zuko doesn’t know where she is for so long.

Does Zuko find her?

Yes. In The Search , Zuko eventually finds Ursa, restores her memories, and learns the truth about what she did and why she disappeared.

In one line

She wasn’t simply “gone” or dead — she was forced into exile, erased her old life, and was later reunited with Zuko in the comics.