Cessationism is the term given to the idea that the miraculous gifts of healing and tongues described in the New Testament were given solely in and for the apostolic era for the foundation of the church and are no longer in effect. The opposite view, continuationism, is that the gifts have not ceased, notwithstanding historical records to the contrary.
The Bible does not either explicitly support or refute cessationism.
Those groups which teach cessationism argue that certain passages in Scripture hint that a time would come where the miraculous gifts as practiced in the New Testament would cease, which the historical record in their view bears out. Specifically they argue that what is called "tongues" today is not recognized as a valid language by any trained linguist, and that so-called "faith healers" (such as Benny Hinn) are frauds (they would not argue, though, that miraculous healings have stopped, only that "healers" who "command" sickness to be gone are frauds).
However, some Christians, particularly Pentecostals and charismatics, argue that the Bible does not support cessationism at all and that the gifts must therefore have continued on, whether or not the historical record gives evidence of them at later times.