That is right, but it's per breaker, so your air conditioner will likely be on its own breaker.

(Assuming 15A fuse, 15A * 110V = 1650W)

Here in Sweden we have 240V from the wall but our fuses are usually 10A, so 2400W per breaker (so we can run Intel CPUs without special installations ;)

Large draw appliances usually get put on a double pole breaker and a house will have many circuits.

He means the standard residential circuit (like you would plug a PC or TV into) is typically 15 amps. Larger appliances, like an AC, are dedicated circuits, usually at a higher amperage. It's not uncommon for AC to be on 30A or 60A