It was a broad view of what humanity could accomplish once their petty differences of race were resolved and the race was looking forward through exploration. The series episodes nearly always involved a serious moral dilemma that the crew would solve through a combination of pragmatism and idealism. The action and comedy of the episodes were merely wrappers around the real message Roddenberry wanted to convey: that if we humans would only just stop fighting each other over trivial nonsense, we could make tremendous progress in exploring the universe around us, revel in the wonder of finding new things we couldn't possibly imagine at the moment, and discover that there are a lot bigger and more interesting things out there that worrying about whose skin happened to be a slightly different color.
The JJ Abrams movies especially simply ignored this basic concept and just went with the action aspect with a little extremely surface glossy history thrown in to make it look just a tiny little bit less like a completely 2 dimensional sci-fi flick of no substance worthy of consideration. As simple standalone sci-fi adventure movies with no tradition or history behind them, they were fairly decent - glossy, amusing, decent action, a reasonable stab at making a futuristic movie look "real" (except for that totally moronic throttle on Sulu's panel), fairly well-done and reasonably well-acted - in short, worth killing two hours of your time for - but they had virtually nothing to do with the original concept of Roddenberry's series beyond the names of the characters.