Basal metabolic rate (BMR) is the amount of energy your body uses per day at complete rest: for breathing, heartbeat, brain and body temperature. It is the largest building block of your total daily energy expenditure. Everyday movement, training and digestion come on top.
How it is estimated
BMR is measured in a lab. In everyday life, equations estimate it. The most widely used is the one by Mifflin and St Jeor (1990), based on weight, height, age and sex. If you know your body fat percentage, there is also the Katch-McArdle equation, which starts from lean mass only: BMR = 370 + 21.6 × lean mass (kg). It often fits very muscular or very lean people better, but it is only as good as your body fat estimate.
Example: With 70 kg of lean mass, Katch-McArdle gives 370 + 21.6 × 70 = 1,882 kcal. These numbers are a worked example.
How accurate it is
In a systematic review (Frankenfield et al. 2005), Mifflin-St Jeor came out as the most reliable equation that does not need a body fat measurement. Even so, it is off by more than 10 percent for some people. At a BMR of 1,800 kcal, 10 percent is already 180 kcal.
What you need it for
On its own, BMR is not very useful for your diet, because you burn more than you would at complete rest. Multiplied by an activity factor, it gives you your estimated TDEE. Do not eat at your BMR for long periods assuming that it is your maintenance: for most people that would already be a sizable deficit.