Il vient d'aller à la piscine.

Does this mean, "I just went to the pool"?

Do you possibly mean? "il veut . . ."

No, it's "vient."

He comes to go to the pool.

The French expression

"venir de" is a special tense that means "just" (in temporal sense), or "a short while ago".

Je viens de terminer mon travail
(I just finised work).
Il vient de me parler au téléphone.
(He talked to me on the phone a few moments ago).

No, the sentence "Il vient d'aller à la piscine" does not mean "I just went to the pool." Instead, it translates to "He just went to the pool" in English. The subject pronoun "il" refers to a male person, so the correct translation would be "he" rather than "I."