Tragedy of the Commons
See Wikipedia. In Game Theory, Tragedy of the Commons is a market failure scenario where a common good is produced in lower quantities than the public desires, or consumed in greater quantities than desired. One example is pollution - it is in the public's best interest not to pollute, but every individual has incentive to pollute (e.g. because burning fossil fuel is cheap, and individually each consumer doesn't affect the environment much).
The relevance to Bitcoin is a hypothetical market failure that might happen in the far future when the block reward from mining drops near zero. In the current Bitcoin design, the only fees miners earn at this time are Transaction fees. Miners will accept transactions with any fees (because the marginal cost of including them is minimal) and users will pay lower and lower fees (in the order of satoshis). It is possible that the honest miners will be under-incentivized, and that too few miners will mine, resulting in lower difficulty than what the public desires. This might mean various 51% attacks will happen frequently, and the Bitcoin will not function correctly.
The Bitcoin protocol can be altered to combat this problem - one proposed solution is Dominant Assurance Contracts.
Another more radical proposal (in the sense that the required change won't be accepted by most bitcoiners) is to have a perpetual reward that is constant in proportion to the monetary base. That can be achieved in two ways. An ever increasing reward (inflatacoin/expocoin) or a constant reward plus a demurrage fee in all funds that caps the monetary base (freicoin).
This scenario was discussed on several threads:
Currently there is no consensus whether this problem is real, and if so, what is the best solution.