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

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.