liquidity can refer to either the volume of trades, or the quoted depth.
In a deep market, such as the S&P or Euribor, there may be thousands of lots bid or offered at the immediate market price - so anyone wishing to put several thousand lots through could easily do so with no slippage or immediate change in price.
That doesnt mean that the market wouldnt react to a huge trade after it had traded.
Depending on your perspective as either a market maker or a trader, there might be opportunities available whichever way you look at it.