Dropping the writ is the informal term for a procedure in some parliamentary government systems, where the head of government (that is the prime minister, premier or chief minister, as the case may be) goes to the head of state and formally advises him or her to dissolve parliament. By convention, the head of state grants the request and issues writs of election for new members of parliament. The usage of the word "drop" in this context is likely derived from the phrase "draw up".
The head of state usually has the right to refuse the request, in which case the prime minister is required by convention or statute to resign. For example, in the case of a minority government, the head of state can deny the request for dissolution and ask the leader of another parliamentary party to form a government. In some cases, such as with the President of Ireland, there are specific limitations on when a head of state can refuse the request. Even then, the right is rarely exercised, as it is likely to precipitate a constitutional crisis (see, for example, the Canadian King-Byng Affair of 1926), and so it is possible that the right of a head of state to refuse a dissolution has become a lapsed power.
Usually, according to parliamentary law, the head of government must regularly call an election but, it is otherwise within their discretion when to drop the writ, up to the time when the parliament has served its full term. At that point, an election must be called by issuing the writs. An exception to this principle is if a fixed-term election law has been enacted.
In some states and territories of Australia, such as New South Wales, Victoria, South Australia, and the Australian Capital Territory, it is normally required by law that the parliament must run its full term before issuing the writs. Early dissolutions are allowed by the Governor (NSW, Vic, SA) or federal Minister for Territories (ACT) only if certain objective criteria are met - in particular, if the parliament is unable to agree on the annual budget. Similarly, in New Zealand, it is the norm for parliament to run full term unless the prime minister cannot govern or feels they must bring an important issue before the nation.
Opposition parties can bring down the government by passing a motion of no confidence, in which the prime minister is required by convention or specific law to either drop the writ or resign; parliaments do not have the right to force the prime minister to drop the writ.
The phrase "drop the writ" is a debased form of the phrase "draw up the writ". Although it is still considered stylistically inappropriate by some, who assert that the correct phrase is, "the writs are issued" or "the writs are drawn up," the phrase is nevertheless widely used in edited copy.