A block grant is a fixed sum of money granted by the federal government to a state government for a specific purpose and subject to certain provisions. The amount of money bestowed by the federal government is determined in advance and if the state's expenditures exceed that amount, they must use their own funds to make up the difference.
The Graham-Cassidy healthcare bill proposes turning Medicaid funding into Block Grants, as opposed to the joint funding program currently in place. Under the current program the federal government and the states split the cost of Medicaid on a percentage basis. This percentage, known as the Federal Medical Assistance Percentage (FMAP), varies by state and ranges anywhere from 50% to 75% depending on the state's per capita income (and certain other criteria).
Under the Graham-Cassidy proposal, states would receive a set amount of money at the beginning of the fiscal year regardless of the actual cost of the Medicaid program, leaving the state legislatures holding the bill if the program ends up spending more than projected. In practice, when states run out of money from block grant programs, as in the case of Community Development Block Grants from HUD, what often happens is the state stops funding the program when the money runs out. If that were to happen with Medicaid it would leave our most vulnerable citizens without essential healthcare service.