State Government
(1) The Governor holds office during the pleasure of the President. (2) The Governor may resign by writing to the President. (3) Subject to the above, a Governor holds office for a term of five years, but continues past that term until a successor takes over.
A Governor formally serves "at the pleasure of the President" - meaning the President (in practice, the Union government) can remove a Governor at any time, even before completing the nominal five-year term. This has made gubernatorial tenure a recurring source of Centre-State political friction, since a Governor can effectively be replaced whenever the central government's political leadership changes.
It's common practice for many sitting Governors to be replaced or asked to resign shortly after a new party takes power at the Centre - a reflection of the "pleasure of the President" doctrine that gives the Union government wide discretion over who serves as Governor.