Lucky number seven
Seven is a key number in the game. Players with 7 points are just a hair's away from winning, especially if they don't yet have the longest road or largest army.
Once you've hit 7 victory points, you're essentially generating resources at an increased rate (since you have more settlements and cities). This increase in resources decreases the amount of time between building new settlements and cities. It also means that you can divert more resources to building the largest army or longest road, and that you're less likely to inititate trade with others because you're more self reliant, be it through just producing more or trading at favourable rates through ports.
Anyone with 7 victory points (without the longest road or largest army) is typically just two to three turns from victory, as they just have to build a city or settlement and either achievement card. I personally choose not to trade with anyne who has 7 points and doesn't hold the longest road or largest army card, unless of course I am in the same or better situation.
It is also advisable not to hit 7 victory points while having the longest road or largest army, since it makes others focus their efforts on blocking you from winning. Despite being quite a few turns from actually winning.
However, if there's strong competition from another player for one of those two cards, it might be prudent to start investing it it from the start of the game.
You should also never end your turn with 7 cards in hand. Remember the penalties.