File transfer

Macs can normally read any disk and its files. However, they may not be able to write to some disks. If that happens, then the disk must be reformatted to a format which can be written to. Which format depends on your Macs OS and how your HD is formatted. Formatting (and erasing the disk) is done with the Disk Utility app.

If the external drive is properly formatted to allow you to write to it, you merely drag said files or folders over to the external drive and they will be copied there. Then you will have to delete them from your iMac.

For what purpose?

(for backup, to free up disk space or for sharing the files with others)