What is a 'classic paper', and when do we refer to a work as a 'classic work'?

This isn't something that is decided based on objective measures - it's a statement of the author's opinion that history has shown the paper to be very important.

If you, in your professional opinion, believe that the paper has had a major influence on an area of research, for a considerable period of time, then you could call it "classic". If you don't believe that, or you're not sure, or you don't think you have enough experience to judge, then don't use the word.

I don't think there really is any one definition of a 'classic' paper, but I think features that might contribute to the label include:

• being an old paper that still gets used (or just referenced) a lot;
• introducing a big new idea;
• having been built on substantially (in a good way);
• being well known as a good survey/suitable for learning the area from;
• dating from and using methods from before a paradigm shift took place.

Note that some of these use the word 'classic' with slightly different meanings.

It is really just a mild expression of reverence by the author. It has no set meaning beyond that.