The easiest way to visualise it is think of a garden hose. The tap is voltage, the water flow in the hose is current and you standing on the hose is resistance.
If you turn the tap on full, you get loads of current flow if there isnt any resistance. If you then stand on the pipe, you get loads of resistance and therefore the current (water through the pipe) reduces. If you turn the tap down the voltage reduces as does the current capability.
Excellent analogy