D&D Armor Class?

So I’m very new to Dungeons and Dragons and need some help. I’m a sorcerer and there are some spells that require a saving throw from the DM. For example, a spell requires a Dexterity saving throw of 15. If the DM rolls a 11, does that mean they fail? If the number they roll is lower than the saving throw requirement, do they fail? If it’s over, do they succeed?

In the same type of question, I have an armor class of 11. When the DM rolls and asks if a 12 "hits", do I say yes? If the number is higher than my armor class, does it hit? If it’s lower than 11, it fails?

Thank you