When I started studying Spanish in 2014, I wrote down a list. I won't call them "goals" because I don't expect to achieve them, and I won't try to draw a line between "intermediate" and "advanced."
1) Reach a level where I could function effectively as a tourist in a Spanish-speaking area where English is not spoken.
2) Have a real conversation, understanding and being understood, with a sympathetic listener willing to speak slowly, listen patiently, and ignore accents and errors.
3) Read simple factual content, such as newspaper stories and articles in the Spanish Wikipedia, and understand most of the content with only a few references to a dictionary.
4) Struggle slowly with novels that use a wider vocabulary, more verb tenses and moods, and "literary" language (e.g. Carlos Ruiz Zafon's "El Sombra del Viento") but succeed in understanding them.
5) Understand the gist of "The News in Slow Spanish" just by listening.
6) Understand a movie, listening to a Spanish sound track and watching Spanish subtitles.
7) Understand a movie, listening to the Spanish sound track only.
8) Understand rapidly-spoken colloquial Spanish, such as talk shows on Univision.
9) Write an iTalk "notebook entry" and have it come back with no corrections at all.
10) Understand the words of Spanish song lyrics.
11) Read novels written in Spanish for pleasure.
12) Understand the meanings and feelings of Spanish song lyrics.
13) Carry on a conversation easily and fluently in Spanish, including abstract ideas and hypothetical situations, with the listener conscious of nothing more than a "charming" accent and occasional strange word choices.
I've tested as "high intermediate" level, and I'd say I've achieved 1, 2, 3, 4, 5, and 11 (but only children's material). I've read 28% of "La sombra del viento." I've improved on #13 but haven't achieved it. I still struggle with "rr."
This is really difficult to answer and I've definitely asked myself the same question before!
The first thing that came to mind for me was being able to enjoy content. I've noticed that when I'm reading or listening to things in languages I'm fluent/an advanced speaker in, I can enjoy the content. There's a movie playing in my head when I'm reading, stories can make me laugh, movies can make me cry.
When I'm reading or watching content in a language I'm learning/am an intermediate speaker in, I'm so distracted by trying to understand and keeping up with the language that the whole experience becomes rather emotionless. It doesn't feel like I'm consuming content for my enjoyment, it's always a chore, something I need to work hard for.
Maybe someone can relate. :P