Story of a Nigeria-born doctor who came to US and discovered that football you have there leads to brain disease called CTE, which you can only prove after you are dead, and about how NFL tried to shut him up. Which, to tell the truth, sounds like a really funny preposition to me, because it's kinda obvious that if you are hitting your head against other people for a living - even if you got the best helmet, you will get fucked up eventually...
Well, no matter. Movie is very dramatic, and stuff, and it follows recent events and discoveries... which are apparently still being argued about. Here, check this article (it has a lot of links in it, too), and then this article, and then this article about real doctors portrayed in movie and this real story summary.
Can you see it? I haven't found any proper mentions about how well Will Smith played the part of that Omalu guy. But in any article you will either see argument about the disease or some sort of opinion about movie and NFL relationship. Quite honestly, I feel like the fight shown in movie is still going, and movie is being not just representation of a story, but additional weapon in the argument.
Well, it does its work well. Will Smith is a very famous actor, and even the idiots will know about it now, cause it's now in the movie. But for determining how true it all is in major events and in details - I guess everyone will have to do their own research.