An important question to ask when selecting a lens for purchase or for a shoot is "What maximum aperture opening do I need?"
Well ... How fast is the subject moving? What is the range of lighting conditions this lens will be used under? What is the maximum ISO speed setting acceptable to you or your customer? How much DOF (Depth of Field) is required?
A wide aperture does a couple of things for you.
Probably the most common reason for requiring a wide aperture is to get a fast shutter speed. Fast shutter speeds stop movement - subject movement and photographer/camera movement as well.
Another benefit (or disadvantage sometimes) of wide apertures is a narrower DOF (Depth of Field). The distracting background can be blurred more easily at wide aperture settings. However, part of the subject might be out of focus if there is not enough DOF.
Lenses with a maximum aperture of f/2.8 or higher allow some Canon EOS camera bodies to autofocus more precisely. Even when you are not using the wide open f/2.8 aperture, the lens still opens to f/2.8 prior to the exposure. The camera's autofocus system takes advantage of the wider opening/extra light. The brighter viewfinder will be welcomed by everyone.
Using extenders reduces the max-available aperture by 1 or 2 stops. A fast lens will retain autofocus capabilities when paired with an extender while a slow lens will become manual focus-only at an effective f/8 (or f/11 depending on the camera being used) aperture.
So how wide of an aperture does one need? Good question - with lots of answers specific to individual situations. I'll make an attempt at some broad guidelines ...
If you are shooting indoors without a flash (or with a fill flash only), you will probably want an f/2.8 or wider aperture. If your subject is still, image stabilization can be a substitute for a wide aperture, but image stabilization does not help stop subject action (IS Mode 2 panning not considered). The wider the aperture available to you, the lower the ISO setting you will be able to use to get your desired shutter speed.
If what you are shooting is indoor action (such as sports), you will likely want an f/2.0 or wider aperture unless your lighting is excellent (this is unusual). An f/2.8 lens is often used in these situations, but generally an ISO setting of 3200 or higher is required to get close to action-stopping shutter speeds.
An f/4.0 maximum aperture is generally good in medium to good lighting. An f/5.6 maximum aperture requires good lighting or image stabilization. And again, image stabilization does not help stop subject action.
If you are shooting landscapes from a tripod, you will likely use only f/8.0 or f/11.0 and narrower apertures. That you lens can open wider does nothing for you.
Adding a flash makes most lenses functional at most apertures as long as the subject is within range of the flash. But, a lens with a wider aperture can capture more ambient light than a lens with a small maximum aperture yielding a more pleasing flash photograph.
Use what you learned here to help you decide which Canon lens is right for you.
Next, go through my specific Canon lens recommendations.