Not sure why @Brick's answer was voted down; let me try to state it more precisely.
maker
Type 1 (seller): You tell the exchange that you want to sell at price P, but P is higher than the highest price at which any Type 2 maker is currently willing to buy. (You're demanding too much money in the eyes of everyone who's said they want to buy.)
Type 2 (buyer): You tell the exchange that you want to buy at price Q, but Q is lower than the lowest price at which any Type 1 maker is currently willing to sell. (You're trying to spend too little money in the eyes of everyone who's said they want to sell.)
Congratulations! Since your request cannot be matched against any existing maker's request, you've just "made" liquidity by adding your desired transaction to the exchange's order book. Your order will sit there until it either gets filled (i.e. someone bites on your offer), expires, or you cancel it.
taker
Type 1 (seller): You tell the exchange that you want to sell at price R, and R is at or below the price currently advertised by at least one Type 2 (buyer) maker. (At least one known buyer thinks the amount of money you're asking for is reasonable.)
Type 2 (buyer): You tell the exchange that you want to buy at price S, and S is at or above the price currently advertised by at least one Type 1 (seller) maker. (At least one known seller thinks the amount of money you're willing to spend is reasonable.)
Congratulations! Since your request can be matched against some existing maker's request, it will get executed immediately (more or less) against the best available maker's price and you will have "taken" liquidity by removing one or more makers' desired transactions from the order book.
If an exchange wants to promote or penalize making or taking it can adjust its fees/rebates for each activity. And it can reduce its fees if you're a high volume customer. That's what the tables show on the web page you linked.