This comes from the research of Anders Ericsson where he measured the amount of practice violinist in a music school had undertaken up to that point. He found that those violinists identified as being elite or experts had put in an average of 10,000ish hours, whereas those who were at lower standards had fewer hours. Therefore, it was concluded that 10,000(ish) hours of deliberate practice would create an expert. I am paraphrasing from memory so some details may be slightly off.
There are a couple of quibbles though. First, the conclusions cannot be transferred from violin to other activities. We can't measure the progress of a musician and determine that a physical sport or a cognitive pursuit would have similar results. Too many variables.
Second, Gladwell takes the generalizations of this study too far. In an interview Gladwell claimed that there was no evidence of an "eternal grafter", someone who practices deliberately and works hard for decades but achieves nothing. But the fact is, the study (if you are to draw Gladwell's conclusions) suffers from selection bias. If I remember correctly, regardless of the skill level, all participants were admitted into the school on merit. So even the lower skilled performers were, by most standards, good violinists. The eternal grafter would not have been admitted into the school.
Third, follow up studies have been done and with many different results. They measured chess players, some reach grandmaster levels after 4000 hours others at 25,000 hours, some were at 25k and counting. Rugby players were reaching professional levels after around 4000 hours. In fact for physical sports, it probably isn't ideal to push to reach 10,000 hours due to the increased risk of injury.
Finally, the whole thing doesn't work as a rule or theory. It's neither provable or disprovable. If I provide examples of eternal grafters, the response is "well it wasn't deliberate practice". Unless we actually get 10,000 hours videotaped, reviewed and verfied of an eternal grafter, we can never prove it wrong. Even that Dan Plan guy who tried it with golf gets criticism that his practice regimen in the last few years wasn't proper.
Essentially, what this 10,000(ish) hour thing works as is a nice illustration of the time and effort high performers put in to reach their standard. We need to constantly push our boundaries, challenge ourselves, open ourselves to criticism, seek out people who make us better and accept that true mastery will take many years of work. That is the takeaway. I would caution anyone against doing a 10,000 hour countdown and just focus on your development and being the best you can be. It certainly shouldn't be a goal line or measuring point.
Here is a video that explains a few of the things I speak of better than I can,
https://www.youtube.com/watch?v=JVXUWWFEXQQ. This gentleman is an expert on talent identification.
I also would like to clarify, that I'm not suggesting all expert ability is based on unmeasurable innate talent. Although I do believe talent exists, I think the majority of talent, particularly as it relates to something like pool, is primarily cognitive. People learn at different paces, but I don't believe anyone should reach an impassable plateau where improvement is impossible (assuming they are completely healthy with no physical impairments).