Ability scores, also known simply as stats, are the most basic 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 just sell a merchant their own shoes. But once you get the hang of it, it’s not that bad to roll these up!
In total, there are 6 ability scores. Strength, Dexterity, Constitution, Intelligence, Wisdom and Charisma. Each of these affects your character in a different way, as jokingly described in the previous paragraph, in order.
Now not all DMs roll this the same way. I personally prefer the 4d6 Drop Lowest method as it leads to more interesting 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 chosen method, you simply 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 (which is 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 who throws other barbarians could be fun)!