The most notorious example is probably Ivern. He's a silly ol' tree, so he seems weak, but he can cast a pretty strong shield pretty frequently. This gives him much more effective health than his health bar and armor/MR would suggest. This occurs to a lesser degree with all shielding champs: unless the shield is very visually noticeable, like a non-generic shield or a very large shield, people don't count it. Oh, that enemy is almost dead! Just one more hit! But then they shield. Break through it or wait. But by the time it's gone, they've regenerated a bit of health and have time to do other things, like reposition or CC you. And by the time that's worn off... maybe the shield is ready again. You might not actually have an opportunity for "one more hit."
Another example is Olaf. Sometimes he has low health. Generally, it takes more work to finish off a low-health enemy than a high-health enemy. But Olaf's attack speed increases as his health goes down, and he has an ability that gives him lifesteal. So as you try to finish him off, he starts hitting you more, and his health stays low (because you're hitting him) but he doesn't actually die (because he's sustaining with lifesteal). This results in people having a wonderful time poking Olaf and watching his health bar fade away, followed by going in and trying to actually kill him, and then instead getting killed by him because his health just kind of stopped going down.
Other examples include standing near walls vs Barn, Ornn, or Vayne; standing near minions vs Neeko or Yasuo; and focusing a champ with a death passive like Karthus or Sion.
I'd say a big part of the reason that pros are pros is because they're a lot better at not just using their own kits, and not just knowing champion kits, but also being mindful of what enemies are capable of beyond autoattacks. I saw a Sneaky clip a while back where he was playing Ashe and kiting a Yasuo, and he was carefully watching what Yasuo was doing, including how many Q stacks he had. When Yasuo fired off a whirlwind, Sneaky was expecting it and Flashed right past it for a kill. Many players would be taken completely by surprise that an enemy did a thing, and would have to rely entirely on their reaction time to that Q3.