Nagware is a software distribution model where the distributed program is free and has all its features available, but the user will be asked to give the developers money. Nagware usually presents itself in three levels. The least obtrusive merely adds a donate or purchase button to a menu or dialog. The most obtrusive pops up multiple dialogs begging for money at regular intervals, often with a timed-delay before you can close them. But the most common nag message is a simple dialog when you launch or close the program asking you to buy it. Nagware is similar to adware, only, the advertisement is for the program itself.
I don't have an ethical problem with nagware regardless of how obtrusive it is. You're being allowed to use a product for free which took someone a lot of effort to make, so an annoying message begging for money is hardly an issue. I'm completely fine with nagware when it's unobtrusive, like in a menu or about dialog. When the nag becomes more obtrusive, like the delay used in early versions of WinZip, it usually causes me to find a different free product, which led me to 7-Zip. My only complaint is when particularly obtrusive nagware is described as "free." I'm generally okay with people calling software "free" even if it has a donate button or a purchase request in a menu option, but when the developer forces the user to see long-delayed nag messages, I see it more as adware than freeware.