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.
Not worth it IMHO.
Can't tell for screens though, I don't even know whether mine does 4k or not. Was part of the home-office package from my company. I'll have to check that tomorrow, only returning from a business trip tonight.