Susan is right: It's the gerund form of "have stolen". The actual tense is in the past - "admitted" - as this is reported speech. Gerunds don't have a time because they function as objects. You use the gerund in this case because "to admit" is transitive. It needs an object, which in this case is the action.

"Admitted"is the main verb and it is in the simple past, "having stolen" is a perfect gerund. A gerund is a verb ending in -ing that acts like a noun. Look at this website; http://www.grammaring.com/the-forms-of-the-gerund

Google Translate syas "Admitieron haber robado el dinero". My Spanish isn't advanced enough to verify if this is grammatical.

What could be the meaning in Spanish?

everything has the reason to exist.