Back in the 1960s and 1970s, aquariums were basically glass boxes with water, colorful dolomite gravel (remember your childhood goldfish bowl?) and rocks for decoration. Sometimes the water was salty (approximating an ocean environment) or there would be a few freshwater plants scattered about, but in essence the only living things in the tank were fish and some bacteria. This was fine and dandy, but there was one major problem: fish, being living animals, had to both eat and poo. Thus, scraps of uneaten food and bits of fish waste inevitably began to foul the water. The ubiquitous nitrifying bacteria would partially colonize the aquarium and convert some of the crud into ammonia and then nitrate, but it all ended up poisonous sooner or later, killing anything unfortunate enough to be living in the water. The only solution was frequent water changes to lower the concentrations of the toxins, and a lot of siphoning to suck out the larger chunks of waste. An entire generation of aquarists were thus condemned to frequent and maintenance, often involving the accidental ingestion of a mouthful of fish-crap-and-decaying-fish-food soup.
The trickle filter was one of the first effective filtration devices designed to clean this type of metabolic waste from the water. The concept is simple: a powerhead pulls water from the tank and trickles it through various filter media. These include filter pads to trap large pieces of debris, bioballs to provide a home for additional bacteria (nitrate is better than ammonia or rotten offal!) and activated carbon to leach harmful chemicals from the water. Unfortunately, the trickle filter doesn't really follow through - the second part of the nitrogen cycle, the denitrifying bacteria that turn nitrates into nitrogen gas, are anaerobic and can't live in the oxygenated waterflow of the filter. Thus, in addition to frequent rinsing of the filter pads to remove captured debris, regular water changes are still required to keep the water livable, and nitrate (itself a poison, although not as bad as some) is always present.
This is okay in a freshwater setup, where the inhabitants are primarily fish and can survive a little nastiness. However, for a saltwater aquarium, it's disastrous. Water chemistry is of the utmost importance to sea life, and constant nitrate contamination rules out the prospect of keeping more sensitive organisms as well as shortening the lifespan of the life forms that can survive. The trickle filter is good for a first-generation tool, but it misses the point - while the surface provided by the filter and a bunch of bioballs is indeed greater than, say, flat pieces of glass and some gaudy gravel, it's nothing near that provided by millions of grains of fine sand or the intricate and multifarious passageways that honeycomb live rock. Thus, at least in a reef environment, it's been almost entirely supplanted by newer and better methods.