A bit confused: what's a HEIF and why do we need 10-bit stills and video?

The latest cameras from most brands are adding 10-bit video (and often stills) capture options. The Canon EOS R5 and R6, for instance, gain both. 10-bit video, 10-bit stills modes and the ability to shoot 'HEIF' files are all features increasingly being added to cameras. But what's the benefit and when should you use these modes? We're going to look at how data is captured, how it's stored and hence what benefits you should (and shouldn't) expect from 10-bit capture. Linear...