Filtration encompasses all we do to make an maintain an optimized seawater medium for our livestock. Discussions of the specifics of filtration are split between what you're trying to remove (e.g. ammonia, nitrate), what gear is used (skimmers, cartridge filters), or the processes (chemical, physical, biological) involved. We will take the last approach in elaborating the terms and tools of most use and interest to marine aquarists.
If any area of aquarium keeping could throw you, filtrations got to be it. Boy (& Girl) there are lots of filter products; and laudatory claims to go along with them. Happily, folks in the West have been keeping marine aquaria since the 1950's with little more than undergravel filter knowledge and practice. Here's another area where you don't have to be an engineer to be successful; don't let the material here or advertisements elsewhere overwhelm you.
In most ways, seawater dis-improves with age, gaining in biological wastes and by-products, while diminishing in buffering capacity, pH, essential trace materials, and Redox potential for example.
This is not the end of the world. Despite what you've been led to believe, the ocean's reefs are not absolutely pristine, nor immutable in water quality. Their inhabitants have corresponding tolerance within a range and rate for different parameters. Similar to freshwater systems, your goal is to arrange for an optimized water chemistry, and avoid quick & drastic changes. For instance, isolating the variable of pH; you're advised to use calcareous materials (gravel, rock, coral and shell skeletons) to buffer pH upward; water changes, circulation and aeration to augment alkaline reserve; avoid crowding and over-feeding, & promote algal growth to limit wastes that drive pH down. But there have been numerous instances of system pH's falling down to and below 7.0 without loss of life.
I mention this to make three points: 1) Don't get lost by focusing on specifics. A drop in pH by itself, or a rise/drop in most factors, is not cause for knee-jerk reaction. You don't want/need to over-react because, 2) Your animals have a capacity to adapt to gradual changes with ranges of tolerance. 3) Modifications should be made gradually; more important than any given point is the rate of change in water chemistry.
The healthier your livestock is to start with, the more drastic changes they can endure. Around the world, I've seen "delicate" marine life swim into freshwater, sewage, garbage strewn areas with impunity. Life is not easy on the reef. Currents and storms are constant, there's more and less light, salinity, oxygen, Redox... Conditions are dynamic, not static.
Your filtration system's function is therefore two-fold; to reduce the amount, effects of wastes, & as importantly, to make the water's chemistry stable.
Depending on what type, size, and livestock you want to keep this is an easy to more difficult task.
As you'll see under the 5) Operation: Setting Up a Marine Aquarium headings, fish only to fish & invertebrates, to full-blown reef systems have increasingly more demanding requirements for "cleanliness" (i.e. an absence of metabolites). Whereas all marine systems would have a functional protein skimmer, fish-only set-ups often get by with little more than an air-powered undergravel filter and/or some outside power filtration.
The presence of non-fish life places narrower ranges on specific gravity, temperature, pH and other 'tolerances'. These systems call for chemical filtrants, more vigorous circulation/aeration, and other mechanisms to reduce water chemistry fluctuations.
Even though I'm only 5' 7", bigger is better (!) in aquarium sizing. Like ocean-size volumes, humungous tanks don't change much very quickly; in part because of dilution, and temperature -wise due to tank wall thickness.
What kinds of life you're keeping touches directly on the issue of the type of system filtration set-up you'll want/need. Reef, cold, temperate or tropical, etc.; and consideration of food use of the organisms' (herbivorous, planktivorous, piscivorous) metabolisms (slow to fast), as well as density (light to too much). Tanks with half as much life in them are easily four times easier to take care of.
Regardless of the type of set-up, filtration, or livestock you have the following applies in terms of system shape, circulation and aeration.
Flatter, shallower, more square systems are easier to maintain than taller, narrower, more elongate types. They are more stable, and have correspondingly larger margins of safety due to the benefits that accrue from having more surface area. Besides, they're easier to work on/in.
Cannot practically be too vigorous. Where you can, agitate your water to the maximum. The movement of natural waters is sometimes incredible, never still. Additional airstones, fluid-moving pumps are great at eliminating anaerobic zones, moving wastes to filters, and speedy processing/removal.
Likewise cannot be easily overdone. Beware of the dangers of too fine bubbles (smaller than 0.1 mm) by limiting their possible exposure within a contactor or skimmer.
in the form of nitrogenous wastes (ammonia, nitrites, nitrates), phenols, scatols and much more is the principal goal of filtration. You might ask (at least I do), "Why don't you see all this filter gear on the reefs in the wild?" Well, you kind of do. Next time you're underwater, take a look around. There really is a lot of water per unit of livestock, and lots of circulation and aeration. Notice the predominant forms of life around you; corals, sponges, bivalves... What mode of food gathering do they employ? They're mainly filter feeders, sieving out plankton, gametes, wastes, suspended inorganic material... that's why the water's so clear. Stuck in and amongst (and inside other life) are algae, some big, others microscopic, utilizing nutrient/making fixed carbon and oxygen through photosynthesis.
Now, let's take a look at a typical marine tank set-up; A small water volume, with lots of non-filter feeders, happily over-fed. Small wonder the battle to limit their waste build-up.
The next subsections delve into filtration methods as principally biological, physical/mechanical, and chemical. All three kinds of filtration occur in all types of filters; and all potential filters you evaluate for purchase/use should be weighed for their efficiencies/manipulation for all three.