Velocity counts how many times a year the average pound is spent
Velocity is how quickly money circulates: nominal GDP divided by the money supply. If the money supply is £500 billion and nominal GDP is £2,500 billion, the average pound is spent on final output five times in the year, so velocity is five. A higher velocity means each pound changes hands more often; a lower one means it sits idle for longer.
Rearranged, the definition of velocity gives MV = PY, which always holds
Multiply both sides of the definition by the money supply and it becomes money supply × velocity = nominal GDP. Nominal GDP is the price level times real output, so MV = PY, where M is the money supply, V velocity, P the price level and Y real output. This quantity equation must hold, because it is only the definition of velocity written another way.
Some courses write the Fisher equation of exchange, MV = PT, where T counts every transaction, including second-hand sales, not only final output. The logic is the same.