Alternative writ [of mandamus]

What does Alternative writ [of mandamus] mean in American Law?

The definition of Alternative writ [of mandamus] in the law of the United States, as defined by the lexicographer Arthur Leff in his legal dictionary is:

A common law writ doing the job more generally done these days by an order to show cause. It was in the form of a command that the addressee take a particular action or come into court to show cause to the court why he shouldn’t, and was in early practice the opening pleading [in] numerous actions. See also mandamus; praecipe.