The way i understand it, by calculating and validating new blocks miners keep the bitcoin network safe. As a 'reward' for this they recieve bitcoins.
However, since the number of bitcoins is limited, will there be a point where mining is no longer useful, because there is nothing left to mine? And if so, who will keep the chain safe?
It is an frequently occurring but incorrect assumption that the purpose of mining is creating bitcoins. The reason mining exists, is finding blocks, so that a global consensus about the order of valid transactions can be established. Mining is hard because we don't want too frequent blocks.
One of the very original ideas in Bitcoin is combining this block construction consensus mechanism with the initial introduction of new currency, but it could have been done in very different ways.
So, even when the block subsidy dwindles and eventually becomes zero, mining will continue. Blocks will still be needed and if miners don't create them, other miners will pop up. They are expected to be paid from transaction fees.
Mining does find new coins, but it also incorporates transactions. So it is expected that mining will still be profitable due to the transaction fees when mining no longer gives coin rewards.
Of course, this won't be a problem for another twenty years or so.
Mining is required for bitcoin transactions to be processed. If mining stops, bitcoin stops.
That being said, Bitcoin generation is only one incentive for mining. The miners also take a small ( << ) percentage of each transaction, and my understanding is that as volume of transactions increases, this will become the dominate method for profiting from mining.
