Most everyone I know of uses the DPS TBC cards with their Toaster/Flyer because it's high quality and fits inside the computer to save desktop space. TBC stands for "Time Base Correction". A TBC is required when feeding an analog video source to the Toaster, but is not required when inputting camera feeds, digital video, or broadcast signals from a tuner or the like.
The reason a TBC is required is technical, but I'll try to explain. Analog VTRs rely on a spinning drum with video heads mounted on it to play and record video signals. Any deviation, however slight, in the spinning speed will produce errors in timing of the signal. Also, tape flaws, vibrations, and other influences will produce timing errors. Timing errors are not good for video, and can't be tolerated by a Toaster. Generally speaking, a TBC will strip the incoming signal's timing and produce a new, clean signal timing which it outputs to the Toaster.
There are other issues that a DPS TBC is useful for - genlocking and signal processing. This is kinda out of the scope of what I want to show here, so I'm not gonna get into it. Also, note that this a a TBCI (the first model they made), and is not used very much nowadays. This is a spare I had laying around; I use a TBCIII in my Toaster. There's not much difference in the physical size, but a lot of difference in functionality, such as the newer ones are software controllable via the Amiga's serial port. When installed in an A4K, the external serial port is required; in an A2K, the internal port can be used.