wants to do~ (third person)
Expresses that someone else wants to do something, based on observable signs.
Use たがる when you are talking about another person's desire or wish. You are not saying what they feel inside, but what they show through their behavior or words. So you can say '彼は行きたがっています' (He shows he wants to go) but you cannot use it for yourself directly, because you know your own feelings without showing them. To express your own wish, use 〜たいです instead.
たがる is a verb, so it conjugates like a regular godan verb. In the present tense, it often appears as たがっている to describe a current state. It is common in everyday conversation when talking about other people's preferences or intentions.