Motor ESC and Battery Amp Draw
The batteries should be rated for the same or higher (continuous) current than the ESC, which should in turn be rated for a significantly higher current than the motor.

The rule of thumb is: Never draw any more current than whatever you're drawing it from can supply.

Also, motors can draw more current than they should. Therefore it's important to include a wide safety margin. Failing to do so could destroy the ESC and/or make the batteries explode or burn. Lithium batteries can be pretty dangerous when abused.