It was a combination of numerous aspects that brought reactor 4 to a close that day, and the eventual shutdown of the entire Chernobyl Power Plant. One of the major reasons being the flawed reactor design (the RBMK reactor), such as the tips of the control rods, that are used to slow down fission rate, being made of graphite.
Graphite is a moderator in fission, meaning it slows down the kinetic speed of neutrons so the fission rate increases, resulting in higher efficiency in the reactor. This can be a problem when trying to lower the power of an RBMK reactor, as the control rods that are trying to slow down the fission rate momentarily spike it. This is what happened at Chernobyl.
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