Someone help explain heart rate monitor calories

Welllll . . . I think there's no magic in a HRM, and it can seriously mislead. (I say this as someone who uses one regularly, BTW.)

Heart rate is a proxy for work effort, not a measurement of it. Heart rate increases when it's hotter weather, when we're dehydrated, when we're excited, when we're straining, and a bunch of other stuff that burns no extra calories.

Those factors make a HRM a pretty bad estimator of strength training calories, for most people: Lots of strain, which raises heart rate, less actual work that burns calories = poor estimate.

I disagree that it's theoretically accurate for interval cardio . . . it can be relatively more or less accurate for any exercise depending on fitness level, which is especially true for intervals. The problem is that what mostly determines calorie burn is the actual work done: A 150-pound person running a mile will burn roughly the same number of calories, fit or unfit. The fit person may run it faster; if they slow down and run it at the same speed, their heart rate will be lower, so the HRM may say they burned fewer calories when they didn't. If the two people do that mile in run/walk intervals, the fit person's heart rate will drop quickly during the walk intervals, while the less fit person's heart rate will stay high through a good bit of the walk portion, and make it look like they're still working hard when they're not. It's problematic.

Also, all HRM are not created equal.

Different models use different inputs and different algorithms to estimate calories. A GPS-enabled HRM would have an input of how far those two people above actual ran, and maybe even how hilly it was; if the HRM's algorithms use that data, it could theoretically produce a more accurate estimate. Does it that use that data? Hard to find out. Does it use the data in well-researched, sensible ways? Even harder to find out.

At the most basic level, a HRM that doesn't know your personal measured (not age-estimated) HRmax is less likely to be accurate, because the age-based HRmax formulas are pretty commonly inaccurate. Without an accurate HRmax, the HRM can't produce an accurate calorie estimate, unless you coincidentally fit the age-based estimates of HRmax. Similarly, if the HRM doesn't know, measure or estimate your true resting HR, it doesn't have a good basis for understanding how hard you're working. Similar issue for your VO2max.

Bottom line: It's all estimates.

Here's the thing: It may not really matter how you estimate your exercise calories, within reason.

Whaaaa?!?!

If you track your intake, and you're consistent (not necessarily accurate) in how your log your exercise, and your exercise itself is at least somewhat consistent . . . then your weight loss results tell the story. Losing too fast, or losing when you shouldn't lose? Increase calories eaten. Losing too slowly, or gaining when you should hold steady? Decrease calories eaten. For most people, consistency in estimating is good enough to make that work.

There can be an exception for people who are eating so little that they get weak and fatigued, so are listless in daily life and exercise: They can lose more slowly than expected, because they've reduced their calorie expenditure but haven't recognized that (it can be subtle). Eating a little more may help their energy level enough to improve their daily-life calorie expenditure and their workout intensity, and perk up their weight loss rate.

This is not saying that if you eat too little your body goes into "starvation mode" and holds onto fat. If that were a thing, no one would ever starve to death, and (sadly) many people worldwide starve to death every day, and they aren't fat when then do so. That "holds onto fat" idea is a myth.

This is good reading about HRM: https://www.myfitnesspal.com/blog/Azdak/view/the-real-facts-about-hrms-and-calories-what-you-need-to-know-before-purchasing-an-hrm-or-using-one-21472

For your HRM specifically, you'd need to read up (or ask the manufacturer) whether it's giving you net calorie burn (excludes BMR) or gross (includes BMR). There's some variation, and in some cases it depends on how you ask (what's in the display vs. what it sends MFP during data exchange). Many/most sources give gross burns (includes BMR).