Size of the boil is how much fluid is in the pot when you turn the burner on.
That, combined with the amount of extract dissolved in the fluid, allows the calculator to estimate the hops utilization percentage, which determines IBU. Say you've got 6 lbs of dry extract, 1 oz of hops at 5%AA that you'll boil 60 minutes. With a 3-gallon boil, the gravity in the kettle is 1.090, and utilization is relatively low; you'll get 13 IBUs from your ounce of hops. Increase the boil size to 5 gallons, the gravity of the boil drops to 1.054, utilization increases, and IBUs rise to 18.
Basically, theory aside, you determine boil size by the largest volume you can boil without excessive fear of boil-over. For my kettle, that's 3.5 gallons. For others, it's 15 gallons! So measure how much you can fit in your kettle. You can safely boil between 60-70 percent of that volume. For example, my kettle is 5 gallons, and I can boil 3.5 gallons safely; that's boiling 70% of the kettle capacity.
You want a vigorous, rolling boil, you see. A simmer with a couple of big "blups" now and then won't cut it. Protein- and sugar-rich fluids at a vigorous rolling boil tend to boil over and make a hell of a mess. So the size of the vessel - and therefore the size of the boil - is based on containment.