Beginner = learning to play
Intermediate = plays well
Advanced = plays flawlessly
Of course, difficulty level is part of it, but not all of it. For example, a beginner trying to play "House of the Rising Sun" will struggle just to make the chords sound cleanly. An intermediate will make the chords sound cleanly, and stay in time. An advanced player will make the chords sound cleanly, stay in time, and also likely add embellishments and subtle variations to their strumming and picking, all played flawlessly. Contrary to popular belief, it has a lot more to do with how you play than what you play. Someone can think they are an advanced player, because they know all their scale modes and a whole bunch of sequences, along with a ton of chords. However, if they can't keep time, or their playing is very stoic and predictable, without any style or flavor, then they really are not going to be considered "advanced". David Gilmour plays solos that are not that complicated in terms of the notes or speed of which he plays. However, very few people can nail the style that he has developed over his many years of playing. Same with BB King.
To consider yourself "advanced", you'll want to be able to play something just the way you hear it in your head, and play it flawlessly. When you have taken an idea as far as you can creatively, and can play it to perfection, then that is "advanced" playing. I know a lot of people will disagree with that, but I've seen so many "advanced" guitar players who have all this knowledge, but they can't play worth beans. Its a bit like diving. The difficulty level doesn't mean anything if you end with a belly-flop!