So I'm going through the rules for the barbarian class, and there's something I didn't get. They keep mentioning proficiency. What exactly is that?
Also, what are all the stats we have to make?
Strength, Constitution, Dexterity, Intelligence, Wisdom, and Charisma, yes?
Correct, Arch. Strength, Constitution, Dexterity, Intelligence, Wisdom, and Charisma are the 6 stats everyone will be using throughout the game.
Proficiency is a way of showing what your characters are "good" at. What makes them unique.
It determines what armor you can and cannot wear. How effectively you make attack rolls with certain weapons, and how specialized you are in certain tasks compared to others (saving throws, tool proficiencies, skills).
This is reflected by a bonus score that you add to all relevant attack rolls, skill checks, and saving throws.
This is called a "proficiency bonus".
At level 1 this starts as a +2, but increaseses as we level up. Everyone has the same proficiency bonus, but it gets applied to different things depending on race, class, and background.
When it says "You are proficient with X", if it's something you would have to roll for, then that's when you add that +2
So for example, you're a Barbarian:
One of your proficiencies is with martial weapons -- a category that your greataxe falls under.
If you wished to make an attack roll with your greataxe, it would be: d20+ strength modifier + proficiency bonus
This reflects your Dragonborn's training with that weapon. You would make a similar roll with STR or CON saving throws and your chosen skills (Athletics for example).
Eladra could pick up that greataxe and use it as well, but since she is Life domain, she is not proficient with martial weapons and can't use that greataxe as effectively (no proficiency bonus).
But she gets her proficiency added to spell attacks and WIS/INT saving throws.
Proficiency is also the reason why Coltshan's fighter is the only person in this party who can wear heavy armor. (Anyone else who might attempt it would get disadvantage on all ability checks, saving throws, attack rolls that involve STR/DEX, and they can't cast spells.)
Or Rona being able to crack an imp's skull bare-handed.