Teleconverters are an interesting proposition: a cheap device you attach between your lens and camera body that gives you an increase in focal length. This great video will give you an introduction to their strengths and drawbacks to decide if they're right for your work.
Coming to you from David Flores over at B&H, this quick video will give you an introduction to teleconverters, which (depending on your needs) can be a great way to get a little extra focal length out of your lenses at a comparatively low cost. They generally come in two flavors: 1.4x and 2x. While they can be a good option, as Flores mentions, there are some downsides. Another thing to know about teleconverters is that besides the autofocus performance and maximum aperture hits, you'll also lose some image quality. Generally, with a good 1.4x teleconverter, the drop in quality is small enough that if you really need the extra reach, the tradeoff is probably worth it. On the other hand, the difference in image quality is generally much more noticeable with a 2x teleconverter, so you'll definitely want to take that into careful consideration before you use one. In general, I think the best situation is when you need occasionally need a 1.4x teleconverter. If you find yourself constantly needing a 1.4x or resorting to a 2x, I recommend considering getting another lens or looking at a crop sensor body if you're shooting on full frame.
I opted for a teleconverter for a bit of a different reason. I had two options to go with for a longer telephoto prime: an EF 300mm f4L IS USM + 1.4x TC, or an EF 400mm f5.6L. I ended up going the TC route because I'd be able to achieve a ~400mm f5.6 equivalent but retain stabilization in the process for about the same price. It also doesn't hurt that the 300mm f4L still performs well even with the teleconverter, of course there's a bit of quality loss but it's really not that bad.
I'm a Canon user and I have a 1.4 and 2.0 TC.
I also have a 3rd party 2.0 TC which works with none of my newer cameras / lens combination. That's a warning too. They may work today but not on the next lens you purchases. Stick with Canon's TC's if you are a Canon user.
The TC's work well on the big whites but not on all the other compatible lens (not every lens is compatible with the TC's)
I would go so far as to say cropping is more effective than using a TC with most lens.
Autofocsing is slower.
The 1.4 is better than the 2.0 performance wise.