The miners are incentivized to mine coins because this way they get keep the coins. It is also important to keep that mining fees is paid whenever a transaction is made on the blockchain.
Whenever a user sends or receive coins they pay a small transaction fees. The thing is that when miners solve a block they verify these transactions and thus get to keep that fee. So the logic is that more fees that you pay for the transaction the miners would be further incentived to include that block in the transaction.
So a higher fees usually also has a better chance of getting your transaction cleared sooner.
The basic math is something like this:
Total block Reward = 12.5 BTC + (fee from all the transactions included in the block)
Note: As the block rewards halfen every four years, the block rewards would get smaller and smaller. In the future the miners main incentive to mine would come from the mining fees.