High drain (IMR) batteries can provide more current than "regular" li-ion batteries. They also have a safer chemistry that makers claim will not vent with a flame.
Running batteries at higher discharge rates than they are designed for will shorten their life (they will lose performance and capacity rapidly from new), give poor performance (voltage droops a lot under load) and could have safety issues. So, high drain batteries allow you to run higher currents with less voltage drop - that is their main advantage.
To expand on this a bit, batteries maximum discharge current is normally expressed as a "C rating". The C stands for capacity, and is the mAh or milliamp hour figure. To work out the maximum current draw from the C rating you multiply the capacity (in mAh) by the C rating.
For example, a battery rated at 1000 mAh capacity and with a maximum discharge rate of 2C, could safely be used for current draws up to 2000 mA (or 2 Amps).
I believe standard lithium ion battery's normally have C ratings between 1C and 2C (not all manufacturers supply this information, but those that do are normally in this range). High quality IMR batteries (such as AW branded) can be rated to deliver up to 10C. A big difference. A downside is that IMR batteries are lower capacity in general - for example on an 18650 you'll get 1600mah for a high drain vs. 2-3000 mah for a non high drain.
Taking a typical 2.5 ohm atty, at 3.7v that will draw around 1.5 Amps current, which on a 350mah 10440 is around 4C. So a high drain battery would likely be beneficial even for running a standard atomiser in the 10440 size. If we look at a low resistance 1.5 ohm atomizer, that will draw about 2.5 Amps at 3.7v (or around 7C for a 350mAh battery) which is way too much for a standard 10440. It would I dare say be 'pushing it' with a high drain 10440, and it would likely be better to go for a mod with a larger battery, such as a 14500 high drain battery, if you wanted to run low resistance atty's.