When you resolve to do something, or when you make a resolution to do something, you make up your mind very strongly to do it. And when you have resolve, or when you're resolute, you have a strong belief that you've made your decision and you're going to see it through.
For example, Kimmy has resolved to go to college. She's made up her mind: she's going to go! It'll be hard work, but she's ready for it. She has resolve. She is resolute about going to college.
A resolution is a promise to yourself that you will do something: usually something good that helps improve your life or other people's lives. I've made a resolution to eat fruits and veggies every day. You might make a resolution to read for thirty minutes every day, or to get outside and exercise three times a week. Or, you might make a resolution to call your grandmother every week, or to always invite any student eating lunch alone to come and eat lunch with you and your friends.
Lastly, here's one more meaning. To resolve a problem is to solve it: to fix it, to find a solution. And a resolution can also be a solution: a way to solve a problem, a way to end a fight or find a compromise. If you and your sibling keep having the same argument again and again, you'll need to find a resolution. In the car, these triplets kept fighting with each other and stealing each other's snacks. Their dad found a resolution: a way to end the fighting. He added partitions!