How do callback urls, tokens work?

Question

HTML

Good afternoon. I'm writing a browser extension, I have a few questions.
The service sends me an API key, which I must attach to the HTTP GET request. It seems clear here, the key needs to be attached to a link of the form:

www.last.fm/api/auth/?api_key=xxx

Further it is not clear, you need to attach tokens, something about md5 encryption, callbacks and the like.
According to the link documentation, there is quite a bit.
If it's not difficult, send articles about how it works, you can even in English, or tell us briefly what needs to be done. Thank you.