I want to upgrade a Minecraft map from 1.13.2 to 1.14.4.
How can I do that?
You put them in the saves folder, start Minecraft 1.14 and select the map.
Ok and I don't break anything there either?
Don't know what should break there. New content is only generated in new chunks, the old world does not change. If you want to be sure, just make a copy of the map beforehand.
If you are unlucky, you will also be asked beforehand whether you know what you are doing. An update from 13 to 14 brings a lot of risk because the meta information has been changed. Make a backup of the world beforehand and if it goes wrong you still have a backup.