Parallels Desktop runs another operating system on a Mac, most often Windows, in a window or full screen. A person can then install Windows applications that do not have a Mac version, without rebooting into a separate partition. The Mac and the Windows desktop run at the same time.
Editions differ by whether they include enough memory and processor settings for heavier programs, and by features aimed at developers or at running Windows from a Boot Camp disk. The comparison is on the Parallels site. A license does not include a Windows license. Windows is bought from Microsoft and installed inside the virtual machine.
Parallels Toolbox is a separate set of small Mac utilities, not part of Desktop unless the page says so. The Mac model and the macOS version that Desktop supports are listed on the product page and change as Apple releases new systems.