Thats awesome - boxing is great fun I love it. Just the two of you or in a class? It's great cardio if you chuck runs and pushups, mountain climbers and stuff in as well. I just got boxing gloves and mits for Xmas so I can do it with my clients.

Here is a bit of info on BMR - honestly it is as importnat that you don't under-eat as over-eat. It doesn't take much for your body to sart storing fat.

What is BMR?
BMR is your Basal Metabolic Rate - in very simple terms, the amount of calories required by your body to sustain life while at rest...

How do I calculate it?
Well, this isn't quite so simple... you can use a very very basic method - simply multiplying your bodyweight in kg by 25 - but this is likely to overestimate your requirement...
A more accurate method is the Harris Benedict Formula:
Men: BMR = 66 + (13.7 X wt in kg) + (5 X ht in cm) - (6.8 X age in yrs)
Women: BMR = 655 + (9.6 X wt in kg) + (1.8 X ht in cm) - (4.7 X age in yrs)
or, if you know your lean body mass (but let's be honest about this, who does?), the Katch McArdle Formula (which is the same for men and women:
BMR = 370 + (21.6 X lean mass in kg)

Why is it important?
Well, like any well tuned engine (or not so well tuned for some of us), if you don't give it sufficient fuel your body will start to shut down! Failing to supply the basic calories your body needs to maintain its status will result in it switching to "starvation mode" lowering your metabolic rate and leaving you drained... And then, when you increase calories, your propensity for storing fat will increase... BOOM, yoyo diet/crash diet effect in action...

So, if I have to lose weight how can I ensure that I've still got a calorie deficit?
Well, this is the easy part... even the most lazy of us aren't at rest for the whole day. So your body's total calorie needs are never just the basic BMR level... Use a multiplier based on your lifestyle to calculate how much you'd actually need to consume (1.2 for relatively inactive, 1.4 for reasonably active (say 3 sessions of exercise per week), 1.5 or 1.6 for more active (say 3 or 4 sessions per week plus a reasonably active job) and even double for those who are extremely active). Create a calorie deficit by giving yourself a shortfall of 500 calories per day without going below your basic BMR... and bingo! Spread those calories over 6 meals a day and your body will never feel deprived...

Hope this helps