This famous post from Tables is often quoted in paraphrasing, but the real post is buried in the middle of a godawful thread and not that easy to search for unless you remember the exact wording so here it is for everyone's convenience.
In Dominion, the objective is not to have the most points when the game ends. The objective to have the game end when you have the most points.
This fundamental understanding of the objective of the game changes a lot of the perspective on how you should play. Ending the game isn't just something which will eventually happen, but should in fact be a part of your goal. In fact, in many engine type games, you might be more concerned with the question of 'can I end the game' than 'can I score points'!
That said, the points obviously still matter. You need to have more of them before you end the game - or a means to get more when you do end the game. Therefore, getting a single Province when piles begin to run low can be a very powerful move. Now your opponent might be able to end the game, but they won't be able to have more points when they do it. Conversely they might end up with more points from their turn, but they won't end the game, giving you a chance to do so instead.
And of course as seems to be always the case in Dominion, edge cases apply. 3+ player games are fundamentally different because someone may end the game as strong second instead of possibly being overtaken. Sometimes (actually not too infrequently) racing to get 1/2 of the points is a better choice than just ending the game - once you have half the points, you can't lose. etc.