First, make sure the drive's contents will fit on the iMac's drive: select the external's drive icon, type Cmd-I (Get Info); do the same for iMac's drive; external's "Used" number must be smaller than iMac drive's "Available." If you're good to go, grab the external's icon with the mouse (left button) and start dragging to the iMac drive; hold down Option key (should see a plus sign appear on the dragging icon) and drop onto the iMac's drive icon. Wait for copy.....
After you're satisfied that files made a good transfer, open Applications -> Utilities -> Disk Utility. Click on the external's icon in the Device column. If you want 2 or more volumes on the disk, click the Partition tab; if one volume is enough, click Erase tab. You don't really need any Options, just click Erase button; done.
Then copy stuff back onto the external; check for good copy; delete from iMac.