One of the commonly touted tenets of OSR play is "diegetic progression"; most character progression is in the world, not on the character sheet. This is why you see a lot weird magic items in OSR resources, stuff that gives particular abilities that encourage creative uses rather than just a + to stats. This type of progression also includes relationships with NPCs and factions that players can call on for assistance. Players don't need to be able to defeat the Ogre in combat if the local chieftain owes them a big favour for rescuing his daughter and will send a squad of his best soldiers to fight it for you/chase it off.

Not having skills on the character sheet is one of the core ideas of OSR play, the idea that players should be coming up with creative solutions in the game and not just relying on the pass or fail of a dice roll to solve problems. Hand in hand with this is, as the above commenter mentions, "rulings over rules" which emphasizes the GM making decisions about how player actions play out in the world rather than looking for mechanics in a rulebook. This encourages stuff like creative tactics in combat, e.g. a player tips over a bookshelf onto the group of goblins; the GM decides the goblins next to it have a 50% chance of dodging out of the way or getting knocked down, or players have advantage against them on their attacks next round as the goblins dive out of the way, etc. There's no rules for this, so the sky is the limit for players to try out cool ideas. Players stop looking at their character sheets and rulebooks when presented with a problem in the game, they engage harder with the game, usually asking questions about details of the situation to see if there is anything they can use to their advantage. For groups that embrace this style of play it is much more immersive than playing a game where your options are dictated by game mechanics rather than the game world.

The most important idea in this, imo, is that a lot of stuff shouldn't even be rolled for; if its reasonable that a player could do it, then it just succeeds. If the players come up with a good idea, just have it work for them unless they are under stress (e.g. hurrying to pick a lock while a boulder rolls down the hallway at them) or there is some adversarial element where an opponent's skill could counteract the player's, e.g. seeing through a player's disguise, avoiding 2 players trying to wrap them in a rope, etc. This really incentivizes the players to think creatively, when their good ideas are rewarded without being at the fickle whims of the dice.