It's really not as bad as it looks, and sometimes this stuff just agglomerates, but each item is a distinct thing. I'm generally of the keep-it-simple mindset, which this person obviously is not. Nonttheless, I've had all of these things at one time or another. I put numbers on the various doohickies in the picture. Here's the reference for what they are:
1: Protein skimmer (foam fractionator) - used to remove organic waste from the water. Of all the items here, this is the most essential. (As with everything, there are alternatives, but you really must have a way to remove dissolved organics.)
2: Hard to tell for sure, but probably a UV unit. Strictly optional - some people actually think they're harmful on reef tanks. (Coral eat tiny animals from the water, and these kill them... This tank appears to be a FOWLR though.)
3: Water bucket... Top off? Automatic top-off systems are important on reef tanks in order to keep the salinity constant as water evaporates.
4: Not sure, but looks like a bio reactor. Use of bio media (organic plastics that are consumed by bacteria and through this, remove excess nitrates) is one of the latest trends. I always preferred using a refugium instead and ended up having more problem with phosphates.
5 and 6: Media reactors - can't tell what's in them, but typically GFO (Granular Ferrous Oxide - for removing phosphates) and carbon.
7: Calcium reactor - helps keep the buffering balanced in the tank. This isn't needed on a FOWLR since there aren't any coral consuming the calcium carbonate to build their skeletons.
8: Skimmate drain bucket. (The skimmer collection cup drains into here.)
9: Supplies. (Looks like media for the reactors.)
In case you don't already know, saltwater tanks are a bit of money pit.
Much more so than freshwater tanks.