Li Shenron
Legend
Tara wants to play a wizard. She can't cast magic, but that's fine, it's just a game. Tom and Jerry are both playing front-line melee of different classes. Jerry used to be a Marine and he can really describe it, Tom ... not so much. But hey, we have mechanics for that and as long as Tom can manage decent tactics we're okay. It's funny, Tom is playing a ranger even though Jerry would be the one who could describe all of the woodscraft. Christine wants to play a half-elven paladin of Corellon; she's a laid back agnostic from a family of them that probably never was to a religious service except for weddings and funerals. Still no problem - it's a fantasy game.
And then we have Harry. He just finished watching Ladyhawke (again), and he wants to play a glib, silver-tongued character. But our Harry is anything but a smooth talker. He's earnest and loyal, but never been good with words.
So what do you do? No one else needs to demonstrate actual skills of their characters - that's what the mechanics are there for. But everyone at the table can convince in character and the closest Harry will get is "I interject a bunch of witty remarks so they like me."
Do you let the mechanics and dice carry him, just like Tara's Fly spell? Do you convince Harry that other people's character concepts can come true but not his, even though the rules allow it? Would you just expect Harry not to ask to play something that so far our of his personal wheelhouse?
This is a made-up example, but how do you, at your table, handle this if it comes up? And the flip side - that player who likes to talk and is good at it but for this character picked CHR as their dump stat and didn't take any social skills.
Dualism between player and character abilities is very normal in a RPG, and I find that it is important to make both of them count.
The exact way how to handle them is less important. In 5e the idea is that rolls aren't always required, only when the DM is actually undecided on the outcome. Most DMs like some randomness, and so they will ask for a roll a lot of times. But they still often just let a player's good idea work.
Personally I think I am quite generous, and I tend to ask for a roll when they have a bad idea, or at least a not very convincing one. The result of this, is that a player who's very good at roleplaying may succeed when her character would fail, while a player who's bad at it will manage through her character's good rolls.
By the way it's not true that this works only for social skills. I have players who know a lot about nature and they come up with great ideas about getting along in the wilderness, even if they play a bookish wizard or urban rogue, and I am sure that military-trained players will come up with the best group tactics in combat even if they play a character that is useless in a fight.
It's very important to not force these players to downplay the game when their character is poor at what they're otherwise good at. Don't tell a smart player to shut up because her half-orc barbarian has low Int (it's ok if she purposefully wants her PC to do something stupid, but that doesn't mean she shouldn't suggest to the rest of the group what's instead a good idea).