An archaism is a word that's so old-fashioned that hardly anyone uses it anymore. Forsooth, you'll encounter many archaisms when you read Shakespeare — or when you go to the local Renaissance Faire.
There's a difference between an archaism and a word that's obsolete, or so out of date that no one uses it. Archaisms aren't dead, they're just archaic, a bit outmoded and best suited to literary or philosophical writing. Shakespeare's plays are full of archaisms, and so are most editions of the Bible. If you prefer to call your friends thou and thee instead of you, you're a fan of archaisms.