The best definition of fluency that I have seen is, "the ability to read, speak or write easily, smoothly, and expressively." So you have become fluent when you can pretty much understand what people are saying and offer cogent and quick responses to what they have said to you, and do this back and forth without unnatural pauses.
That isn't to say that it is presumed that you can follow along with, say, a graduate level seminar in quantum physics. The simplest threshhold of fluency could involve speaking at about a second-grade level. You could still have large holes in your vocabulary that you are adept at working around; it's just that you can understand and respond without it seeming like you are struggling.
As an aside, though, I think of a grade level as more of an allegory than a precise measuring tool. An adult will usually not speak on a second-grade level, strictly speaking. Second-graders, can, for example, describe a lot of household items and know verbs that an adult might hardly ever use, like "to cluck" (gdakać). How many times as an adult are you going to be called upon to say, "The cow moos?" But a second-grader could tell you that easily. Still, since it's not all that useful for you to know how to say that, learning to say things like this should be low on your list of priorities. And, as an adult, you might know the word for "sociology" (sociologia) or "empathy" (empatia) relatively early on in your studies, especially if the related word is a cognate to the more complex concept that a second-grader might not necessarily know.
So there exists what I call basic fluency on the low end, and then native fluency on the other end. Native fluency is what you would expect your average person who grew up in the country that speaks the target language to have. And it can be uneducated native fluency at the low end and highly educated native fluency at the high end. Most foreign speakers don't get to highly educated native fluency, ever. There are individuals who do, either because they are particularly gifted in language acquisition, or because they work like crazy to eliminate all the little errors in grammar and syntax, and deficiencies in their accents. Many people who learn another language often have little grammatical errors or stilted modes of speaking in which sentences are constructed like they might be in a different language. But note that grammatical (or spelling) errors occur even with native fluency. Some are a part of colloqualism, and some run with a dialect. And some are just common mistakes that native users of a language make. Ain't a lotta English natives cain't figger out whut this sentence mean. You see spelling errors in English all the time whereby some people use the wrong form of [it's or its], or [they're, their or there]. Other languages have little traps like that too.
Fluency doesn't just take one path; native fluency is just the most ingrained path. Here is where it branches out. You can have contextual (usually occupational) fluency. This, at the low end, is where you might be able to communicate with a co-worker or an owner might be able to communicate with a hired hand using terms that are commonly used associated with the work (usually this type of communication is more faux-fluent that "real" fluent). At the high end, it could be the specialized vocabulary that is used in, say, the medical or legal fields, or that a geologist or orchestra member might use.
I am fluent in Spanish. I can communicate easily and freely in that language. I would come somewhat short of saying, though, that I have native fluency. I have a lot more than basic fluency. I can communicate easily in speech or on the phone (speaking on the telephone is often a step up for language learners because they don't have the visual cues any more), with hardly any linguistic work-arounds. I can understand almost everything I hear on TV, though sometimes I have to concentrate. I can understand most words in the newspaper, though I would probably have to look up words much more often that I would have to in English. So I still have room for improvement (but then again, I do even in English). Have any of us really completely learned any language, even our own native language(s)?
I wrote a follow-up post on fluency here.