Body fat percentage is the share of your total body weight that is fat mass, given in percent. The rest is lean mass: muscle, organs, bone and water.
Example: At 82 kg and 18 percent body fat, you carry 82 × 0.18 = about 14.8 kg of fat. Your lean mass is 82 - 14.8 = 67.2 kg. This is a worked example.
How to estimate it
At home you cannot measure body fat in the strict sense; you estimate it. Common options are tape measure formulas like the US Navy method, body fat scales and estimates from photos. These methods can differ by several percentage points for the same person. Scales with electrodes also depend heavily on your hydration. So only compare values from the same method and pay more attention to the trend than to a single number.
What you need it for
Body fat percentage is the key number for deciding whether to start with a bulk or a cut. As a rough rule of thumb from practice, not from studies: men above about 20 percent tend to start with a cut, men below about 15 percent with a bulk; for women the thresholds are roughly 8 to 10 percentage points higher. The direction behind it is backed by research: the more fat you carry, the less lean mass you get out of a surplus (Forbes 2000).
You also need body fat percentage for FFMI and for the protein range during a cut, which is based on lean mass. Measuring every two to four weeks is enough; more often you mostly see measurement error.