This is THE most difficult concept to grasp in Airflow. After you get this the rest of the system is fairly straightforward. But this one design spec is brutal, I have seen it being seasoned engineers to their knees, sobbing in fits of rage.
As the other poster mentioned in the Airflow docs, Airflow runs your job at the end of the period. This is easiest for me to visualize for a DAG that has a daily schedule. The DAG run date for 01/01/2021, with a start time of 00:01 AM, will not execute until 01/02/2021 00:01 AM.
The confusing part of this is WHY!? When you stop to think about why Airflow was written it begins to make sense. This execution pattern ensures that the data for the run date 01/01/2021 is complete and ready when your orchestration pipeline runs to act on this data. Think about it as a business process. If you are a business analyst and come into work on 01/02/2021 you will be looking at data from the day before, not data from today. The data from today has not yet been collected.
The same pattern is true for weekly or monthly intervals as well. The data for that week or month is not going to be ready to act on until the end of the period.
This also makes more sense when you start using the macros and jinja templating.
Hopefully this is now clear as Mud.