Simplified (it used to work this way, now it's slightly more complicated), each television channel frequency required a certain small range (the tuner frequency +/- a certain number of MHz) to carry its signal. Ideally, the affected range of spectrum wouldn't exceed that specced amount, but electronics aren't perfect, and RF is a tricky matter.
In practice, you tend to see splatter near a particular channel, outside its allotted frequency range. Furthermore, receivers have to filter out any signal not within the frequency range for the channel they want to watch, but the filtering circuitry (called a bandpass filter) will tend to cause distortions within the intended frequency range the better they are at filtering frequencies outside that range. There are also other complicating factors, like signal overloading receivers, and mis-tuned transmitters.
This resulted in a margin space between channels, so that adjacent channels would interfere with each other less. As receiver electronics have gotten better, more selective and more error tolerant, these margin spaces became less necessary, and we have space in the spectrum that's no longer required for its original purpose of providing a margin.
That space is your 'whitespace'.