Learn Hardcore Hungarian: Annak ellenére, hogy esik, az önkéntesek összegyűjtik a hulladékot. - Even though it is raining, the volunteers collect the waste.

As a whole, annak ellenére, hogy means despite the fact that, even though, or in spite of the fact that. It introduces a clause that contrasts with the main action.

So here, it sets up the contrast: Even though it is raining, the volunteers collect the trash.

How is annak ellenére, hogy built grammatically?

It is a fixed expression made of three parts:

annak = of that / despite that in a form required here
ellenére = despite / in spite of
hogy = that, introducing a clause

A very literal breakdown is something like despite that, that..., but in natural English you should think of it simply as despite the fact that.

This is a common Hungarian pattern:

Annak ellenére, hogy fáradt, dolgozik.
Even though he is tired, he works.

Why does esik mean it is raining?

The basic meaning of esik is falls. In weather expressions, Hungarian uses it for rain, so esik by itself usually means it is raining.

So the idea is basically: rain is falling → it is raining

This is one of those everyday expressions you just learn as a set phrase.

Why is there no word for in ?