In contrast to an Internal filter (where the bulk of, or entire, filter sits underwater in the tank) there are at least 3 very popular external filter general designs currently: the "HOB" (Hang On Back) filter, the "Sump" filter and the "EC" (External Cannister) filter.
In all three cases, the filters use "siphon" action to enlist gravity to do part of the work (and to have the pump do the other part and keep it going) of extracting water from the tank and into the filter chamber. Because you don't want the water to move too quickly tthrough the filter media (and because it would require a larger and not incidently noisier) motor) the water pump nearly always requires additional attention to get the siphoning action started (either through more expensive automatic design or some extra attention from the aquarist.) So siphon action takes the water out and pump action puts it back in the tank and keeps the overall process going.
Now, specifically, I'm going to assume you were really asking about an External Cannister, which differs from HOBs and Sumps in that they are both open to the air, while the EC is sealed. An HOB has just the very short distance over the tank edge as it's siphoning job. A sump is like a second aquarium sitting below the main tank and usually moves progressively through different media types in a sideways movement, finally using a submerged pump in the final chamber to pump the water back up the output tube.
But an EC (External Cannister,) is sealed, allowing it to simply stop and stay put when power is lost (as long as it stays sealed) and not require as much elaborate attention to safety against accidental outsiphoning and overflow from the tank. It also makes it quieter than the Sump or HOB because the smaller high-frequency water surface noises are sealed away.
Like the other types, the chambers or trays for different media types can be arranged in different ways, typically with bottom to top, side to side or top to bottom internal water flow. In most cases (if not all) the water is "pulled" through the media by the pump's impeller, rather than "pushed." A typical design would be to passively pipe the water from the intake hose (where there is often a manual "shutoff valve" down to a bottom empty chamber (where large debris can accumulate,) following which the water is pulled through coarse and then increasingly more fine types of media in often one to four "media trays." Multiple media trays are one of the hallmarks of the flexibility of the EC design, allowing aquarists to insert and removed custom media choices with ease. For instance, temporary use carbon, zeolite, Purigen, crushed coral bags or other highly specilized or chemical media can go in and out with hardly any disturbance of other media beds.
The EC also often excels in terms of media volume, a fundamental principle of filtration. The larger the media bed, the more thoroughly the water will be exposed to the media, giving the media more time to trap debris and perform other functions. Sumps, of course, often carry this aspect even farther. Another little appreciated aspect of external filters is that they represent an effective increase in the volume of water available to your fish (beyond the volume of the tank) from the water chemistry point of view (as opposed to swimming room.) Filter box volume is often associated with the design types (internal smallest, HOB next, EC next and Sump largest) and reflexively applied in this order to smaller to larger tanks, but it doesn't have to be this way, as a larger external filter can be applied to a smaller tank as long as the flow rate can be dealt with in some way (for cost efficiency though, there is not much flexibility in this aspect and most higher volume designs are also limited to higher tank flow, limiting them to larger tanks etc.)
The EC often represents an advance in ease of maintenance over the Internal or Sump designs in that the first stage of disconnect from the tank and removal to the sink room can be done either without getting wet or can be done easily at all. Quick release mechanisms to disconnect both hoses at once (and leave them filled with water and ready for re-priming) are common in EC designs. Note that "priming" (the establishment of water continuity between the filter box and the tank within the output hose) does need to happen with external designs. Note also that placement height (or perhaps I should say negative distance) is usually an important EC filter specification that should be understood.
So, in popular and more simple terms, an External Cannister often represents a beginners evolution into a somewhat larger tank and more intermediate/advanced gear for that tank (but there are certainly exceptions to that thought.) The EC usually has higher media volume, higher flow, more ease of maintenance and more media flexibility than what the beginner has grown used to in their typical first small tank with internal or hood filter. There are pros and cons to every filter design, but the EC has earned it's place in the current state of the hobby.
~~waterdrop~~ (morning coffee mode
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edit: (now would someone please come along and tell him how the darn thing works
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