High liquidity means that the market has a large turnover of money, which means that the player can place a bet in this market, and a large one, and it will be accepted by another player (if the proposed odds are be optimal).
Low liquidity implies little or no turnover at the market rate. Hence, a player can make only a small bet that will be taken by another player, or just can not trade at all.
The highest liquidity has a betting exchange Betfair.