A grant of arms or a governmental issuance of arms is an instrument issued by a lawful authority, such as an officer of arms or State Herald, which confers on a person and his or her descendants the right to bear a particular coat of arms or armorial bearings. It is one of the ways in which a person may lawfully bear arms in a jurisdiction regulating heraldry, another being by birth, through inheritance.
Grant by Clarenceux King of Arms Robert Cooke to Henry Draper of Colnbrook giving him the right to use the arms illustrated; dated 14 October 1571. Source: The National Archives UK
Swedish grant of arms from 1562.
In heraldry, an augmentation is a modification or addition to a coat of arms, typically given by a monarch as either a mere mark of favour, or a reward or recognition for some meritorious act. The grants of entire new coats by monarchs as a reward are not augmentations, but rather grants of arms, and an augmentation mistakenly given to someone who did not have a right to a coat would be nugatory.
Some of the Juliusbanner given by pope Julius II to the Swiss cantons and their associates included augmentations or "improvements"; shown here is the banner of Rapperswil, with the two roses of the city's coat of arms rendered in gold instead of the usual red.