Donationware is software that is free to use, but encourages users to make a donation to the developer. Some donationware programs request a specific amount, while others allow users to determine what the program is worth and send in an appropriate donation. Unlike shareware, which may provide limited functionality until a registration key is purchased, donationware is fully functional. Therefore, donationware is more similar to freeware, which is free to use, but retains the author's copyright.
Some donationware programs make subtle requests for donations, such as an option in the menu bar. Others are more blatant, and may prompt you for a donation each time you open the program. This dialog box should disappear once you have made a contribution. Most donationware programs allow you to donate to the developer via a credit card or PayPal account.
If you find a certain donationware application program to be useful, you can be sure the developer will appreciation your donation. Just make sure that the website you use to donate is legitimate and provides a secure (HTTPS) connection.