Beginner - someone who is just beginning speedcubing
Common Traits: Most beginners have very slow recognition/recall and spend up to half of their solve time looking for pieces/recognizing cases. They rarely use inspection time well, maybe just find the first piece or two of cross/2x2x2/1x2x3. They make mistakes almost every solve and sometimes are forced to go back to an earlier step in their solve and start over.
Intermediate - someone who is getting better and faster, but still needs a lot of work and could easily improve in most every facet of their solve
Common Traits: Many intermediate cubers have moved on past their original beginners method to a faster method that often times means more algs. If they are a CFOP user they have probably moved on to basic, intuitive f2l and some variation of 3/4 Look LL. Intermediate cubers are better at using inspection, and can maybe plan out most of their first step, but not always. There is still a lot of time being wasted simply looking for pieces, but not as much as when they were beginners. Mistakes are made, but relatively infrequently.
Advanced - someone who is very good and very fast, and can only shave a second or two (mebe 3) off of any given step in there method
Common Traits: Advanced cubers almost always know a full speedcubing method and can recognize/recall all of their algs quickly. Most of their solves will have no long pauses, few cube rotations and almost no major mistakes. They can use inspection time to completely plan their first step, and sometimes more (track first f2l pair, xcross, 2x2x3). Many advanced cubers know additional sets of algs that can make them even faster when the situation arises (COLL/VHF2L/OLLCP/NEOPLL(lol))
Expert - someone who has nearly pushed their method to it's limits and has almost no where left to go in order to improve.
Common Traits: everything that advanced cubers do but better. Almost no recognition time, near-perfect lookahead. No pauses, almost no rotations, just perfect, fluid solves with very high, consistent TPS. Many algs are known, duplicate algs are known and experts know when to use which alg to get the best next step, i.e. an expert knows when using a certain OLL alg will force a PLL skip, or when to use a certain f2l alg to force OLL skip. There are no cases that slow them down, an expert CFOP user will know tons of advanced f2l tricks such as multislotting, using open slots, wrong slot algs etc.