In horticulture, a graft is where the tissues of one plant are affixed to the tissues of another; the process is called grafting.
In medicine, the same term is applied, particularly often for skin grafting, but also for other body tissues moved and re-joined: coronary artery bypass grafting (CABG), bone grafting such as in vertebralfusion procedures etc... See medical grafting.
In politics, graft is a form of political corruption whereby someone profits personally from the public budget.