Gravenstein is undoubtedly a very old variety, and its origins are confused but there is clearly a strong association with northern Germany, Denmark, and Norway where it remains very popular - in 2005 it became the National apple of Denmark. In the 19th century examples were taken to both New England and California where it is still widely grown.
Although Gravenstein has never achieved great commercial success, it remains popular with apple enthusiasts around the world. The flavour, both for eating fresh and (especially) for cooking is unusually good for such an early-season variety.
Like most early-season apples Gravenstein does not keep that well but, usefully, the apples tend to ripen individually over the course of a couple of weeks so you are not necessarily faced with a sudden glut. (This lengthy ripening time is one of the reasons Gravenstein is not successful as a commercial variety, but is a plus for the home orchardist).
Gravensteins have a distinctive flushed colouring, which begins in mid-August as a few streaks of red, and spreads to cover the whole apple by the end of the picking season in mid-September.