Runes are a form of writing used by witches and wizards hundreds and even thousands of years ago. Some important magical documents are written in runes, and some magical items have runes inscribed on them. Ancient runes are studied at Hogwarts by those wishing to be able to decipher and interpret inscriptions and writing by magical people of long ago.
Two kinds of runes appear in canon. The truly ancient runes are found on the Pensieve; they are described as "modified Saxon runes" (Pm). These runes would be very angular since they were indented to be carved into stone and therefore would not have curves. These runes date back to the Viking invasions circa 500 AD. The others appear more as pictograms, related in shape to natural objects. These consist of circles, lines, and small pictures. Beedle the Bard appears to have been written in this form of runes (JKR:Tw, JKR).
Old Norse: rúnir, rúnar ‘magic signs, hidden lore.’
From the Web
Write your name in runes on PBS.org: learn the forms and meanings of early Viking runes.