Critically, the HDMI 2.1 spec is tasked with supporting "higher video resolutions and refresh rates" across the board. 8K resolutions will be supported at 60 fps, while you'll be able to pump 4K content at up to 120 fps. In fact, resolutions can be cranked all the way up to 10K, which we're assuming will be at 30 fps.
New Ultra High-Speed HDMI cables will be able to support up to 48Gbps of bandwidth (for comparison's sake, Thunderbolt 3 tops out at 40Gbps), which will be capable of channeling uncompressed 8K HDR video. This new cable will be backwards compatible with existing HDMI-compatible devices.
Other features supported include Variable Refresh Rates (which we in the computing world equate with NVIDIA G-SYNC and AMD FreeSync); Quick Media Switching, to eliminate blank screens that may occur before content from movies are played; and Quick Frame Transport to enable lag-free gaming and virtual reality content. Dynamic HDR is also supported.
With 4K TVs, gaming consoles and media streamers just now becoming commonplace (along with the accompanying 4K content), it will be quite a while before we'll be banging down the door for 8K-compatible devices. As for 10K content, we may be well into the next decade before we even start trying to wrap our heads around devices that will be capable of supporting such crazy-high resolutions.