> i thought it would good bye because you guys use it at the end of a letter doesn't make sense to end a letter with a greeting

You could translate it as "good bye" at the end of a letter or message, or as "regards" or "best wishes" or something like that. There are a few variations.

kveðja (singular)
kær kveðja (singular; kær = dear)
kærar kveðjur (here the plural is used)
*bestar kveðjur (plural; this one tends to be avoided)
bestu kveðjur (plural)

The dictionary definitions use more general words like "greeting" or "salutation" because it has more varied uses than English "good bye", and these words cover more of those meanings. That's to say, it isn't only used at the end of a letter in Modern Icelandic or in Old Norse. In fact, Cleasby/Vigfússon's examples from Old Norse included some where it was used at the beginning of a letter. I agree we don't normally end a letter with the word "greeting" in English.