Attributes are described only in a generic sense. How they come into play is up to the DM. The better they are, the stronger your character is in that regard.
Three types of rolls depend on these values - ability, saving, and attack.
Numbers range from 0 to 30. 10 represents an average human. 18 is a general character maximum. Monsters and divine critters can hit 30.
The number determines a modifier via
floor((score - 10) / 2). For example - 10 is 0, 5 is -3, and 18 is +4.
If these apply, you roll two dice and pick the highest/lowest respectively.
Some characters have this bonus based on their level. The bonus is added once to a roll.
These rolls occur when 2 or more actors are trying to do the same task (think tug-of-war, or opening/closing a door).
Skills represent a specific aspect of an ability score. Players can be proficient in a skill.
If the skill applies to the check and the player has the skill, then their proficiency bonus applies to the check!