Adding a bit to this...The venturi effect works to pull draw in water from inside your tank; thus increasing the amount of water that is moved in the aquarium. The velocity of the water is also increased because of the small nozzle; pressure increases and then pushes the water faster through the narrower opening.
The Venturi effect is in use in more places in our tanks than most people realize. How many of you have a protein skimmer? If yours has a tube that comes up to pull in air, you already have a Venturi in your tank. It has been said in bits and pieces already, but I thought it would be good to have the details in one spot...
So what happens in a Venturri? Here's a picture to help:
On the left (point 1), water is entering from a return pump and flows freely until it hits the narrowing in the tube (point 2). When it hits this point, it causes the pressure at point 1 to increase. Notice the little vertical tubes? They are showing the pressure differential between point 1 and point 2. The pressure is higher at point 1, so the liquid level is higher. Where get benefit is from what happens as a result.
Starting on the left...
Remember from your science classes the conservation of energy? It states that energy in equals energy out, in its simplest form. In the case of this Venturi, the pressure on the left increases, which causes a decrease in pressure on the right. The increase in pressure on the left causes a decrease in the volumetric flow rate of the water through that section. Think about this like head pressure. You get less return flow when you have more head pressure.
Looking at the right...
Since the pressure went down on the right, the water is freer to flow here so the volumetric flow rate goes up. The pressure at point 2 is lower than the pressure in the tank so the water flows in to equalize the pressure. In the case of these accelerators, they open up the sides after point 2 to allow water to get pulled in.
OK, so now we know what causes these things to happen, but what happens in the tank? You will see an increased volume of water moved around in your tank over the same period of time. We call this increased flow. It is the same principle as a Vortech or Tunze powerhead. They don't introduce more water volume, they just move more water around.
Side note, the water level in your sump will go up using one of these(unless you have a controllable pump and make adjustments).