It's an old wives tale that we don't use but a small fraction of our brain. While there are probably a handful of cells that seldom if ever get used it is only a very small percentage.
We can't, of course, claim that we use it all at all times; the brain rests sometimes, too. In addition parts of the brain do different things and if current activities don't require the use of those sections they may be temporarily inactive.
The bottom line is that we basically use all of our brain, not 20% of it.