Yeah, I get it and how it could be cool, I just haven't played anything like it and have a hard time not thinking it's weird.
It actually helps give even more of a sense of progression with your character than most video game RPGs could accomplish.
Take my first D&D character, a Dwarf Rogue. Now, as she gains levels, of course she does more damage, gains HP, and increases her hit accuracy and AC (Armor Class, basically a Attack roll must match or exceed its target’s AC).
But in addition to that, she has her skill options, which are affected by your character’s stats (which can increase at certain levels) but also you can choose skills to be proficient in (based on your class and background) which give an additional bonus and also your proficiency bonus goes up at certain levels.
So my Dwarf Rogue is proficient in Stealth, Perception (these first two get even more boosted due to the Rogue class letting you boost two particular proficiencies), Deception, Insight, Investigation, Persuasion, and Thieves’ Tools. So all these skills will get boosted as her level goes up.
So as she gets stronger, she not only improves in combat, but also:
-(Stealth) hiding from enemies, which also can be used to massively boost her damage and give advantage on attacks (meaning you roll twice and use the higher result)
-(Perception) spot hidden people, items, spot something in the distance, etc.
-(Deception) lie to people
-(Insight) determine if someone is lying
-(Persuasion) convince someone with an argument
-(Investigation) search rooms, drawers, chests, a huge pile of notes, etc.
-(Thieves’ Tools) unlock locked chests, doors, etc.
And there are around 20 skills overall. It shows your character progressing in a way that extends well beyond combat. The dice roll represents no one is perfect though. Sometimes another person refuses to change their mind. Maybe someone has a perfect poker face. Maybe you might have spotted that figure hiding to your left but a fly got in your face and distracted you. This is the beauty of D&D, you will become far stronger as you progress, but you never become perfect in every possible aspect of life, even the things you train specifically in. But you will become far more frequently successful in those specialized skills.