I want to delete messages on my macbook air but not my iphone

If you just want to delete the big-ticket items that have been sent in Messages, follow the steps:

1. Go to the Apple logo on the top left of the screen
2. Click on the section labeled 'About This Mac'
3. Go to the storage tab
4. Click on 'Manage...'
5. On the left, there should be various sections, and one should be labeled 'Messages'. Click on that
6. Now click on the files that are taking up a lot of space, and if you want to select multiple files, just click on one file, then, while holding the shift key, click on another file. That should select multiple files
7. You can now create more space on your MacBook Air

PS: If you were just referring to deleting the app itself, this is not possible; however, this would not create more space as the Messages app only takes up 8 MB (differs on different computers)