Resting metabolic rate (RMR) is the energy your body uses when you're doing nothing at all — keeping your heart beating, lungs breathing, brain working, and body temperature steady. Basal metabolic rate (BMR) is a slightly stricter laboratory version measured under controlled conditions; in everyday use the two terms are close enough to be interchangeable. RMR is normally the largest component of total daily energy expenditure, with the rest coming from digestion, daily movement, and exercise.
It matters on a GLP-1 because RMR is largely set by how much lean tissue you carry. As weight comes off — especially if muscle comes off with it — RMR drops, and it can drop a little further than body size alone predicts (adaptive thermogenesis). That's why protecting muscle with protein and resistance training, and re-checking calorie targets as you lose weight, both matter. See calories in, calories out on a GLP-1 and do TDEE calculators still work after big weight loss.