It's true that it is the LOAD that controls current flow, not the SOURCE
Here's an analogy...
On your house, there is a water valve that you use with a garden hose right? When you crack it open completely, you get a relatively light stream of water. Dad washes his car with it, maybe mom waters her roses.
However, if a fireman opens the hydrant at the roadside, you get enough water coming out to push a parked car backwards.
The source of the water pressure for both is the same water tower.
So to answer your question more exactly --- Your power supply COULD output 5V at 3A IF the load wants it. Your load doesn't. Your load will only allow the 240mA that it wants to pass through it.
Voltage = Water Pressure
Current = Quantity of water
Resistance = size of the opening we're letting the water out
Now personally I kinda HATE the water analogy because it doesn't describe many electrical phenomena, so don't take it too literally!!! Electricity does NOT flow like water. Yes there are electrons that move in the wire, but the REAL energy is in the electromagnetic field that surrounds the wire --- But don't get buzzed on that quite yet, you have alotta time ahead of you to get confused about this stuff ;)