Sure I do not have a ton of experience with skimmers, but do have a basic understanding of how they work.
So, as you probably know, a normal filter will handle mechanical and biological filtration. I feel I should mention here that a lot of saltwater tanks don't have a ton of biomedia, if any at all. This is because the live rock in the tank is hosting beneficial bacteria and can therefor maintain a cycle.
In smaller saltwater tanks with HOB filters, some like myself choose to modify the HOB so it can also work as a refugium... lol. A refugium, or fuge is simply a place where macroalgae like chaetomorpha can be grown. Water flows through the fuge, a plant light is used, and as the chaeto grows it uses up excess nutrients like nitrates and phosphates. This is a form of nutrient removal.
Running a skimmer is another form of nutrient removal. Water will move through the skimmer, but it's air that's doing the work here. Tiny bubbles will form and rise up into the collection cup, bringing dissolved organics, (the stuff that turns into nitrates and phosphates), with them. Skimmers need to be sort of broken in, or more accurately, tuned. Users need to fuss with the settings at first, working with flow and air until the skimmer is producing sludge... the brown slimy stuff that is the dissolved organics. The sludge will collect in a cup at the top and the aquarist will have to empty it every so often.
Personally, I run a 20g closed system, (no sump), nano reef with an Aquaclear 70 HOB that has some biomedia in it, but is mostly used as a refugium with mechanical filtration. Skimmers are great, but not always necessary. It depends upon your goals.