Graft can mean bribery or corruption. It's also a way of transplanting skin or bones in medicine, as in a skin graft.
People who get terrible burns on their faces often have pieces of skin taken from other parts of their bodies to help them heal and look better. That transplanted skin is called a graft. There are also grafts in agriculture, when farmers take a branch from one tree and graft it onto another tree. The most common use of graft is in political corruption cases when politicians are accused of taking money in exchange for granting favors.