Ability scores, also known simply as stats, are the most fundamental part of your characters in 5E, barring paper, dice, and personality (in all forms). Without them, you can’t know how easily you chuck dwarves, avoid falling down steps, process taco bell, memorize pi, turn ferocious beasts into pets, or sell a merchant their shoes. But once you get the hang of it, it’s not that bad to roll these up!
There are six ability scores: Strength, Dexterity, Constitution, Intelligence, Wisdom, and Charisma. Each of these affects your character differently, as jokingly described in the previous paragraph, in order.
Now not all DMs roll this the same way. I prefer the 4d6 Drop Lowest method as it leads to more exciting builds, but your DM might have you use Point Buy or Standard Array instead, depending on how they DM. The methods and how to calculate when using them are as follows:
For Standard Array, you get a fixed set of numbers, typically 15, 14, 13, 12, 10, and 8, though you might want to use a different array should your DM allow it.
For the 4d6 Drop Lowest (also known as Rolling), you roll four six-sided dice, then remove the lowest (e.g., 6, 5, 3, 1, drop the 1 for 14), recording the result, and repeating for each ability score.
For the Point Buy method, you start with an 8 in everything and 27 points to spend. If a score is below 13, you may spend 1 point to increase it by 1, and anything above that requires 2, though it’s usually capped to 15 in calculators.
Regardless of the method you use, you choose which score increases. Once you follow the steps for the selected method, you add any racial bonuses, and your ability scores have been rolled! One last thing to note: for every 2 points in an ability score, you gain +1 to the ability modifier (0 at 10, 1 at 12, 2 at 14, etc.), which is used for almost every ability check and saving throw.
Now that you are freshly armed with this knowledge, go and conquer with a character that makes you happy (perhaps a barbarian throwing other barbarians could be fun)!