Is it important to have the different legs balanced? I have never heard of checking this...
I assume that L1 and L2 are the two 120v lines that come into the fuse panel?
Yes, out on the pole is a transformer, it has a primary winding (city side) and a secondary winding (house side), the secondary winding is center tapped to earth(imagine a 240 inch 2x4 marked at the center, say the 120 inches above the center mark is the L1 phase and the 120 inches below the center mark is L2 phase) Each phase has a limited amount of current it can supply.
Generator (240/120) has same thing more or less transformer but even more current limited, say a 7KW gen. So each 120VAC phase (L1/L2) is then 3.5KW, 30 amps/120VAC phase or 30 amps at 240VAC ........
If your house uses 7KW. Say you have a 240VAC water heater takes 4KW(17 amps) This then says the combined L1/L2 120VAC (L1/L2) loads must be around.....3KW/120VAC = 25 amps
And COULD be around 12.5 amps for each phase, no sure yet ........L1 has approx 1.5KW (12.5 amps @120VAC) available and L2 will have 1.5KW (12.5 amps @ 120VAC) available.
What if though, your 120VAC things (L1/L2) aren't balance? Say of that 3KW, L1 is 2.5KW and L2 is 500W?
Again, L1 (and L2) sees from the water heater load is 4KW/240VAC = 17 amps and in our example, then L1 = 2.5KW/120VAC = 21 amps. So 17 (water heater) + 21 = 38 amps! L1 is overloaded!! The breaker will be popping off.....
But, If you "balance" (move) the 120VAC loads around such that 1KW goes over to L2 from L1 so each phase is now around 1.5KW , then 17 (water heater) + 12.5 = 29.5 amps.