What are Checkpoints and Milestones?

When you are about to start a night or when you click on your profile picture, you will see a timeline with checkpoints and milestones.

1. Checkpoints:
Try to reach those by all means. Checkpoints are your savegames in this game.
When you get defeated at night, you will start again from the latest checkpoint. Your whole village will be repaired and you get a set amount of resources. You can also choose some of your survivors for the next try.

2. Milestones:
On milestones, you will get a certain reward like a new survivor or a resource bag. Please note that milestones are not always checkpoints/savepoints.
The game tells you exactly when you will reach the next savepoint. 
Look for the "Next Checkpoint: Day XX" to know how long you need to survive before you reach the next checkpoint.