Lava rock is meant to be a bio-media, in that it provides a surface for beneficial bacteria rather than "filtering" in the sense of clarifying water by capturing particles. Lava rock is highly variable and often not the most efficient in terms of surface area per volume.
I have this piece of coral rock with lots of powers on it.
Did you mean pores?
3 main types/functions of filter media:
Mechanical media-- Acts as a strainer to physically remove particles and debris, sponges, foam pads, and filter floss do this, some canisters use a type of ceramic rings to theoretically improve flow through the filter and trap some heavy debris.
Bio media-- Provides the surface area where beneficial bacteria can live. All manner of materials can be used, specialized ceramic, sintered glass, etc., various aqaurium sponge and foam products, other (non toxic) foam, sponge, etc., including pot scrubbers, to mention a few. So sponge and foam does both (technically, so does poly fiber if you leave it in long enough). The point of being porous is to provide a lot of surface area per volume of media, which is where a lot of debates start and where some materials are better than others. Fiber/carbon cartridges tend to be minimally efficient (and less cost effective) vs most other options.
Chemical media, like carbon-- Removes medications and some chemicals and organic substances (not ammonia or its derivatives). As mentioned, carbon has a limited useful life that varies according to how much you use, which type, what you're trying to remove, etc. Chemical media is optional in most cases.