Lean body mass is your body weight minus your fat mass: muscle, organs, bone, water and glycogen combined. In everyday use and in most calculators it is treated as the same thing as fat-free mass. Technically the two are sometimes distinguished, because lean body mass includes a small amount of essential fat. For your planning, that difference does not matter.
How to calculate it
Lean body mass (kg) = body weight (kg) × (1 - body fat (%) ÷ 100)
Example: At 80 kg and 20 percent body fat, that is 80 × 0.8 = 64 kg of lean body mass. This is a worked example.
The number is only as accurate as your body fat estimate. If that is off by a few percentage points, your lean body mass shifts by several kilograms.
What you need it for
During a cut, lean body mass is what you want to protect. Helms et al. 2014 recommend 2.3 to 3.1 g of protein per kg of lean mass for lean strength athletes in a deficit. In the example above, that would be about 147 to 198 g of protein a day. FFMI and the Katch-McArdle formula for basal metabolic rate also start from it.
During a lean bulk, its trend shows whether your gain comes mainly from lean mass. A simple sign without any math: if your weight rises while your waist barely grows, you are mostly adding lean mass. Keep in mind that water and glycogen count too. A step after more carbs or creatine raises lean mass on paper without adding a gram of muscle.