Bitcoin fees are an incentive for miners to include your transaction in the next block. All transactions that haven't yet been included in a block are contained in the mempool, and there are typically more transactions waiting in the mempool than can fit inside one block. This means that some of them have to wait for subsequent blocks to be mined.
The amount you should pay to get priority processing varies based upon the current congestion of the Bitcoin ecosystem. Most of the time, you'll get your transaction included in the next few blocks with a fee of less than $1.