I'm confused

Your TDEE is more or less what your body burns on average in a day, according to your height, weight, job, yadda yadda. Eating about 20% under that it a good way to determine a range in which you'll begin to lose weight. The number you should calculate is your BMR because that's the Minimum number of calories your body needs to function - so you DO NOT want to eat below that.

I would say you would want to eat either between your TDEE and your BMR or right around your BMR. I'm roughly the same height as you and started out a little bit heavier for weight. I'm down 27 pounds eating at my BMR which is about 1445. Sometimes I eat my exercise calories back and sometimes not. It just depends on how hungry I am. I listen to my body and give it what it needs. I'm loosing weight slowly but I like it that way because I'm learning how to eat healthier and normal portions and this will be sustainable when I reach my goal and switch to maintenance mode.

MFP will also give you your TDEE.
MFP doesn't factor in your exercise (unless you have your exercise in your activty level)
some other sites do

Have a look at what MFP is giving you for TDEE.

check you entered everything correctly, weight height and age.
if your TDEE is 2000 your daily should be nowhere near 1200 cals - should be more like 1500

MFP says I should have 1200 calories plus exercise calories each day. I have seen several people post about TDEE so I went to a site that had a TDEE calculator and my TDEE is 2115. My question is how does the TDEE thing work? Should I stick to the 1200 calories or just try to keep calories below my TDEE? I am 46 years old, 5'3" and currently weigh around 186lbs. . I have been eating 1200 plus exercise calories and have been losing about a pound a week. Any help will be much appreciated.

My stats were like yours in February. I had no idea (and frankly was a bit confused with alot of the terms) so I just ate what MFP told me to and then ate back my exercise cals. just like MFP told me. I bought a HRM Pf7 for accuracy. I weighed and measured my food, "learned the MFP bible and lost all my weight by the beginning of the summer. Took a bit of a summer break, but ate according to what I had learned and never gained. Now Im on a second goal weight. And doing it the MFP way.