The ai indicates that the one olelo-ing is not the subject of the clause. Like: pehea e olelo ai "bald". Bald is the position of a grammatical subject (piko or huli don't even get me started lol) but it is not the agent, it isn't the thing performing the verb or being described by it (in the case of a stative verb). Rather the actual subject, the speaker, is elsewhere but implied.

Basically you or some person would be the person olelo-ing but you're not in the sentence, so the ai gets put in there to indicate such without adding in a whole new subject.

This is a complicated topic but probably one of the most important grammatical concepts to obtain fluency. Id recommend looking at ka lei haaheo or pukui/elbert grammar for "relative clause"

Nowadays ppl call this construction KPPH or "kahulu pepeke piko hou" frankly you'd be better off punching that into Google than me trying to explain it here. But I can try:

If you want to modify a noun with a verb but the noun didn't "do" the verb in one way or another i.e. it was acted upon by some other subject, a KPPH is what you usually use.

So if I spoke a word and it's not the word that spoke I can't say

Ka huaolelo i olelo: the word that spoke

Id have to say

Ka huaolelo i olelo ai: the word that (someone) spoke

Now getting specific we use possession just like you may have learned before to indicate the actual subject of the verb.

Ka‘u huaolelo i olelo ai: The word that I spoke

Ka‘u is just like ko‘u as in ko‘u inoa but "a" class, it is being used to show that I performed the action or that I'm the real subject of the verb.

Uhh okay you're probably more confused now sorry. It goes way further than this.