I have a 4k TV and don't get it either. Watched the odd video in 4k and the colors are maybe a bit crisper, but that's about it. I'd have to compare movies side by side to actually spot the difference.
The point of 4k is that you can have a TV twice as large as your 1080p TV before it without losing sharpness.
I can definitely tell the difference on my 77” OLED.