The homegrown rule requires clubs to fill part of their registered squad with players trained domestically for three years before the age of 21. It is a quota on squad composition, not on nationality, so a foreign player who came through an English academy still counts as homegrown.
The nationality point is the one most often misread. A player born abroad who joined an English club as a teenager and spent three seasons registered there qualifies, while an England international who spent their entire youth career overseas may not.
The Premier League applies it through a squad list capped at 25 players, within which only a set number may be non-homegrown, with under-21s registrable separately and outside the cap. UEFA runs its own version for European competition, which additionally reserves places for players trained by the club itself rather than merely in the same country.
It shapes the market in a way that is easy to see in fees. A competent homegrown squad player is worth more to an English club than an equivalent foreign one, because the quota makes the registration itself scarce, and domestically trained players carry a premium as a result.