When creating a market, the creator is given the opportunity to set a maker and taker fee. Likewise, these terms are mentioned when participating in a market. What do these terms mean?
The other answer is correct in how it defines Maker Taker fees, but it should be made clear that Augur does not have Maker Taker fees anymore. The current UI is a bit out of date with reality, but Augur (the contracts) now only charge fees on share settlement (consider opening another question about "when are fees collected" or "in what ways cans hares be settled" for a more detailed answer).
These concepts stem from traditional trading.
When a market is open, the number of open orders in its order books represents its liquidity. Much liquidity represents much activity, thereby making the market more desirable to participate in - much like you'd prefer there to be a lot of people on an online multiplayer game server, rather than just you.
When opening and closing positions, a trader can be either a maker or a taker. Those creating orders are makers, and those filling them at market prices are takers. For example...
When buying or selling at market prices - meaning, placing an order in such a way that it's filled immediately - you will be taking some orders off the order book, because you'll be filling them. Fewer orders mean less liquidity for the market, and therefore you'll have to pay a taker fee (you took some liquidity away).
When placing an order such that it does not currently meet the needs of market prices (i.e. you're waiting to either buy or sell at a given price you expect to occur in the future), you're a maker, because you made an order stick around in the books - you made more liquidity for the market.
Typically, taker fees are higher, while maker fees are lower, nonexistent, or even endorsed with rewards like discounts on commission.