Error question

Ok, the issue may be the type of cable you are using to transfer the data. As you are already aware, your MBA has Thunderbolt 3/USB-C ports. The iMac, on the other hand, has both USB-A and Thunderbolt 2 ports.

I am assuming that you are attempting to do this transfer using Apple's Target Disk Mode ... correct? If so, double-check the steps in the following support article to make sure you didn't miss anything.

Ref: Transfer files between two Mac computers using target disk mode - Apple Support

How exactly are you trying to connect this MacBook Air to your iMac? For what purpose? Which exact models are both of these Macs?

Thanks, but it will still be helpful if you can provide the exact model numbers for each of your Macs.