I recommend you to get a good multimeter and start measuring around - you can learn a lot of stuff by experimenting.
For example, try measuring the short-circuit current if you connect the probes straight to the battery terminals in ammeter (10A) mode. You'll probably see much more than 500 mA, but only briefly. The same goes with other battery types - for a fresh alkaline AA you can briefly get around 10 amps (which is almost 5 times their capacity, around 2000-2200 mAh).
Why is that? First of all, we're comparing apples and oranges; if a cell stores say 2000 mAh, it means it can deliver 2000 mA for one hour, or 200 mA for 10 hours, or 10000 mA for 12 minutes. That's in theory. In practice the chemical reaction inside can't happen that quickly and the current will quickly diminish, while the battery gets very hot and things get quite dangerous. If you're measuring short-circuit currents, please use caution and only do that briefly.
This, combined with what Andy aka said, answers your question. Your motor requires some serious current when it starts, because the rotor needs to have power inserted into it to start turning. Your battery happens to be capable of providing that initial burst. Once the rotor is moving, its inertia keeps it that way and you only need power (much less power, actually) to overcome the friction and other losses, which aren't that large. Again - get a good multimeter and measure the steady-state current, I believe it will be much lower than 1.9A.