Theirself is a singular, gender-neutral pronoun used as an alternative to the plural-sounding themselves or to the gender-specific himself or herself. Theirself is used in instances when the gender of the subject is unknown or when the subject has a gender identity other than male or female, such as nonbinary.

How do you use themselves?

You use themselves to refer to people, animals, or things when the object of a verb or preposition refers to the same people or things as the subject of the verb. They all seemed to be enjoying themselves. You use themselves to emphasize the people or things that you are referring to.

Is their self grammatically correct?

In traditional English there is no correct singular form of this non-word; instead of “theirself” most people use “himself” or ”herself.” If you encounter “themself,” it's probably not a mistake but a deliberate choice to avoid specifying gender, following the pattern of using singular “they” for the same reason.