Explain BMR to me

This is incorrect. Basal Metabolic Rate is TDEE - about 20 to 40 %

It is the energy needed to sustain autonomic systems.

BMR + activity + thermic effect of food = TDEE or maintenance.

Actually, we are both right. What I quoted is RESTING, without exercise.
In most topics, TDEE is what you are quoting - BMR is the NORM to Maintain

Also, you are ADDING to BMR to get your TDEE :laugh:

Basal metabolic rate (BMR), and the closely related resting metabolic rate (RMR), is the amount of energy expended daily by humans and other animals at rest or sleep . Rest is defined as existing in a neutrally temperate environment while in the post-absorptive state. In plants, different considerations apply.
Also see: basal metabolic rate an expression of the rate at which oxygen is used by body cells, or the calculated equivalent heat production by the body, in a fasting subject at complete rest. Abbreviated BMR. (This is MEDICAL terminology for BMR.

Former Medic in the US Army. As pertaining to this discussion, I would lean more to my answer. Yes, I am biased.

About 70% of a human's total energy expenditure is due to the basal life processes within the organs of the body (see table). About 20% of one's energy expenditure comes from physical activity and another 10% from thermogenesis, or digestion of food (postprandial thermogenesis).[10] All of these processes require an intake of oxygen along with coenzymes to provide energy for survival (usually from macronutrients like carbohydrates, fats, and proteins) and expel carbon dioxide, due to processing by the Krebs cycle.

Mads, can you give me your age and height, please? I presume you are a man and your weight is 210 lb, right?

Basal Metabolic Rate

It's the minimum amount of calories that your body requires to function without any extra movement. Think about coma patients-- They aren't moving or using up extra calories to talk or move. They're completely sedentary, but their bodies still need enough calories to breathe and keep the heart pumping. If you're in a coma, the hospital will feed you your BMR requirement-- no more, no less.

We can survive on fewer calories than our BMR requirements because we do have extra fat stores to pull energy from for a limited amount of time-- and that's what causes weight loss. However, you shouldn't eat below your BMR for extended amounts of time because your body will only dig into those fat stores for so long before it will break down muscle for fuel, and when you break down muscle, your metabolism will slow down because it needs fewer calories to maintain your body.

Edit:
MFP is programmed to calculate your TDEE (total daily energy expenditure), and remove 10-15% of that to cut calories. If you set it to sedentary, your TDEE isn't going to be very much higher than your BMR, so removing that 10-15% might be below your BMR. The only restriction on the calculator is that it won't tell anyone to go below 1200 calories because that's what they have deemed to be the average "safety" limit.

But if you're serious about losing weight, don't just rely on cutting calories. Exercise more, lift weights, build muscle. Fuel your body enough to sustain a more active lifestyle.

Related -- this is a subject of confusion to me, as well: If, according to MFP, my BMR as a 29/131-lb. female is 1,288, why is MFP then assigning me only 1,240 calories per day?

It depends on what you're telling MFP. It won't go below 1200, but it also won't say, "Hey... you should aim for a half pound a week at this stage of the game."

Sorry, not meaning to "split hairs." As I see it, 48 calories is 48 calories, I don't want to unintentionally not give my body what it needs (else I'd not have asked)... Simply trying to understand how this all works.

you can customize your calorie intake in the settings. bump it up to 1,300 calories, but honestly, even that feels too little to me. how tall are you??