The short explanation
A progressive frame is a complete picture. An interlaced field is half of one: the odd lines, then the even lines. Two fields make a frame, so 1080i60 is sixty fields and thirty frames per second.
On a modern flat panel the two fields have to be woven back together — deinterlacing — and how well that is done varies enormously between devices.
Where you run into it
Broadcast television still carries interlaced formats, and so do older recordings. If motion looks combed or soft, the deinterlacer in the chain is the suspect, and which device does the work is worth controlling.
1080i is also not a lesser 1080p: it is a different structure that needs processing, which is why the two behave differently.
How the DR HDMI 8K handles it
The DR HDMI 8K passes interlaced formats including 1080i and 480i, and its EDID library contains dedicated 1080i60 4:4:4 8-bit tables. Because it does not scale or deinterlace, it leaves that work to whichever device you decide should do it — and the EDID is how you steer that decision.
Want to test your own HDMI chain?
The DR HDMI 8K is sold through the HDFury.eu web shop.