Yeah, this does get really confusing. Hear's how it works: Your "baseline metabolism" is the amount of calories you need to just keep your body functioning. In other words if you were in a coma, you would need somewhere around 1300 calories.
Now assuming that you are not in a coma, but that you move around, take a shower, fix a meal, take out the trash, etc. The additional 554 calories that you see in the "activities" section takes into account how many calories you need to accomplish your daily activities (without exercise).
This is where a little experience can be very helpful. For many women the activities calcualtor tends to over estimate the number of calories we burn. Therefore using the lower of the mifflin vs. harris calculations helps as does choosing an activity level that is a little more seditary. Some people do, indeed, add in sleep which helps lower the calorie requirements.
Once you get an lifestyle/activity level that seems about right for you, then you can add in your exercises, including things like mowing the lawn or picking up after the kids.
I hope that helps a little. There is a little more art than science to these calculations since everyone is quite different, but after a while you learn at what calorie load you lose weight, and when you begin to pack the pounds back on.