You did not tell us which MacBook Air and you did not tell us which macOS you currently have and to which macOS you are updating to. You also did not tell us how much free space you have.
I will have to therefore provide an answer that is completely based on guesswork.
You generally need about 40GB - 50GB to download and install a macOS update (based on a Big Sur update). If you do not have enough free space on your MacBook Air then you will have to create it. This is done by deleting data on your storage drive. Media files take up the most space and therefore I would begin by deleting unwanted videos, photos, music etc. You can then review your documents folder and see what can be deleted and then finally delete the apps that you do not need.
I am also assuming that you have created backups of the Videos, photos, music, documents and apps.
Axel F.