If you bet a side at -110 and it closes at -125, your number beat the close. That's CLV in one sentence. Over a large enough sample, players who beat the close are net-positive after vig. That's the part that's true.
Three places CLV lies: thin markets where the closing number is manipulated by a single late move, props that close hours before kickoff and never re-open, and futures where the closing line is months away and your number was right for a season that already moved on. CLV is a scoreboard, not a result — confirm it with a profit curve before you trust it.