Let's look at it from basics:
The battery, by way of a chemical reaction, provides an electromotive force (EMF) because of the potential difference (PD, measured in volts) between its terminals.
Electrons in the wires, bulb and resistor are moved due to this force (because they are charged particles). The quantity of this movement is called current.
The lower a resistance something has, the more easily the electrons in it can move, and so the current will be higher (for the same PD).
The battery only has a certain capacity of energy (which is being used to drive the current through the conductors, and is dissipated in them) and so will run out. the more current (thus more energy) involved, the quicker the battery runs out.
Does that help?