The runes are letters. That is the first and most important thing to say about them, because almost everything else claimed for them is later, and the epigraphic record is large and unambiguous.
The Elder Futhark is the oldest complete set, twenty-four characters, named from the sound values of its first six, and it is attested on inscriptions from around the second century CE across the Germanic-speaking world. It was adapted from an Old Italic alphabet, which is why several characters look like recognisable Latin letters. It divides into three groups of eight, the aettir, and each character has a name, Fehu cattle or wealth, Uruz the aurochs, Thurisaz the giant or thorn, Ansuz the god or mouth, and so on, recorded in rune poems written down in Old English, Old Norwegian and Old Icelandic, considerably later than the inscriptions themselves.
As the languages changed, so did the alphabet. Scandinavia reduced it to the Younger Futhark of sixteen characters by the Viking age, which meant a single rune had to serve several sounds; England expanded it to the Anglo-Saxon futhorc of up to thirty-three. Runes continued in ordinary use well past Christianisation, the Bryggen finds at Bergen include hundreds of medieval inscriptions on wood, and a great many of them are business notes, name tags, love messages and obscenities.
That last point is worth dwelling on. The surviving corpus of runic inscriptions is overwhelmingly mundane: this person made this, this person owns this, this person is remembered here. A minority are charms or invocations, and a handful are genuinely obscure. The picture of runes as a body of magical script that happened also to be used for writing is not what the material shows.