Let me put it to you this way:
Think of pressure in League of Legends like a ripple effect in a pond. At the start of the game, for the most part, you're all little waves traveling accross the surface. In order to get bigger, you get kills, or put pressure on your opponent laners.
Now imagine there are structures, some heavily defended or hard to get early (dragon, or a tower defended by a ranged carry and a CC support, or baron) and others easy (kills, CS leads, or vision control). In order to get Dragon, baron, or bot lane tower, you need to be a BIG wave, because it's a thick piece of wood that needs a good slapping, but killing top lane is like breaking a blade of grass, or ganking mid which is like breaking a twig while also giving your other friendly wave a boost.
Now, there are two bigger waves comparative to the enemy, making it easier to take on bot lane, that thick stick in your way. Let's say you now kill the enemy jungler, now you're a gigantic wave, traversing to bot lane with your mid laner. Now what would have been you just blowing their summoners early game and cracking the gigantic stick has turned into obliterating that enemy stick, getting a turret and a dragon, and now having every lane snowballing along with you. Your team is now one gigantic fighting force of a wave, going for the biggest structure, mid lane tower.
See? That's a good visual.
You're right though, putting pressure bot lane is definitely how you win games in this META, but that doesn't mean you mindlessly throw yourself at the enemy bot. You have to go about it tactically.