As the block reward diminishes over time, eventually approaching zero, the miners will be less incentivized to mine bitcoin for the block reward. This could be a major security problem for Bitcoin, unless the incentives provided by the block reward are replaced by transaction fees.
Transaction fees are some amount of Bitcoin that are included in a transaction as a reward for the miner who mines the block in which the transaction is included. Transaction fees are voluntary on the part of the person sending a transaction. Whether or not a transaction is included in a block by a miner is also voluntary. Thus, users sending transactions can use transaction fees to incentive miners to verify their transactions. The version of the Bitcoin client released by the core development team, which can be used to send transactions, has fee minimum rules by default.