My MacBook air is not syncing with my MacBook Pro, things like bookmarks, photos, music, etc

Syncing works via iCloud. In another message you indicate that other devices are syncing so unless you are seeing syncing issues with the other devices the problem is probably between your MBA and iCloud. Typically this solves the problem. Open System Preferences on your MBA and open the iCloud tab. Click on Sign Out in the iCloud tab. You'll be asked if you want to keep a copy of the information from a couple different sources on your computer's hard drive. Let's take a look at that in a second. Answer yes or no to this question and let the sign off continue. Now your computer is no longer connected to iCloud. Now sign back in. Depending on how much data needs to be synced you may need to let the computer sit (and awake) for a few minutes or a few hours. But once this process has finished your syncing problems should be over. You can test by bookmarking something on your MBA and seeing if it shows up on your other devices. Then also test by book marking something on another device and see if it shows up on the MBA. (We want to test both directions.)

I put off talking about the copying because it is a bit complex. If there's anything on your MBA that hasn't been synced to the other computers then yes, you want a copy left on your computer. If everything on your MBA is also synced then don't bother with leaving the copy.

We would need many more details to help you.

Why would you expect a "sync"? Do you, for example, use iTunes Match or Apple Music, and therefore expect the same music on both devices? Do both Macs use the same Apple ID with iCloud turned "On" and System Preferences > iCloud > Safari turned "On" and therefore expect the same bookmarks on both devices?

What have you done to make you think these things would sync?

Why not sync my bookmarks etc. to your Mac instead of yours? Syncing does not just mysteriously occur. Syncing typically occurs between an iOS device and a Mac (or PC) when the device is plugged in to the computer and connected to iTunes.

If your iOS devices sync without connecting, either you use Wi-Fi sync or store your material in iCloud.