A video format that defines at least a billion distinct colors, for greater contrast and detail, usually noticeable in the darkest and lightest parts of a scene. (Non-HDR video is limited to 16.7 million colors.) HDR10 also mandates a minimum display brightness.
HDR10+ adds metadata to dynamically control display brightness / tone mapping. This allows darker scenes to have even more detail.
Standard video has 8-bit depth, which means 256 levels of brightness for each of the red, green, and blue primary colors. Mixed together, that makes 16.7 million color possibilities. HDR video has 10 bits of depth, for at least 1,024 levels of brightness per primary color, for at least a billion total colors. HDR10+ allows up to 12 bits, for even more colors.
A phone may have an HDR10-capable display — meaning it can properly show HDR10 video — and/or may be able to capture HDR10 video with its camera. Phones that have an HDR10 display are not necessarily able to capture HDR10 video, although many high-end phones have both.