The number of devices you can install the software depends on the number of licenses you've purchased.
If you've purchased a single license for AirParrot 3 for Mac or Windows, this is good for one computer. The number of users on that computer are unlimited. If you've purchased for example 5 keys, you can install the app on up to five computers. Again, the number of users on a computer is unlimited.
If you have a computer that runs multiple operating systems (either by dual-booting or using virtual machine software), you will need one license for each operating system.
AirParrot 3 for Chrome OS is user-based. Once you purchase a license, that license will follow your Google account to any Chromebook or Chrome OS device you log into.
Reflector for Android works similarly. Once purchased, it can be downloaded on any device your Google account is logged into.