The project was born out of frustration with DOS incompatibility with the various versions of Windows available circa 2000. Microsoft later dropped support for 16-bit software completely in 64-bit versions of Windows. DOSBox provides a means of continuing to enjoy older Windows games that cannot be run under current versions of Windows by running Windows 3.1 or even Windows 95 inside DOSBox (yes, the compatibility is that good).
Anyone used to using DOS will be right at home with the DOSBox shell, which not only implements most DOS commands, but also includes the ability to change the configuration from the DOSBox command-line using built-in "programs" (although most users will probably just edit the dosbox.conf file in a text editor).
The official distributions do not support functions like printing, given that the emulator is geared toward gaming. The developers have also cited no interest in emulating a SoundBlaster AWE32/64 card, arguing that the Gravis UltraSound (which is emulated by DOSBox) produces far superior sampled sound, despite repeated requests from users. Of course, given that the program is distributed under the GPL, you can always make your own custom patches and compile if you need to.
Another advantage the program has is the ability to support modern USB joysticks and gamepads within the older programs. And even if a game was never meant for them, you can use the program's built in mapper (accessible by pressing ctrl+f1 on your keyboard) to add the ability.
DOSBox has proven popular with commercial developers who originally wrote their games for DOS and have started selling them again.
Apogee Software's games available through their online store also come with DOSBox if the game doesn't run natively under Windows.
When Bethesda re-released The Elder Scrolls: Arena and The Elder Scrolls II: Daggerfall for free on their website, the updated installation instructions for the games explicitly stated you would need DOSBox.
Also, whenever GOG.com re-releases PC-DOS classic games of past times, you can expect it to be possible thanks to DOSBox.
You can download DOSBox from http://www.dosbox.com/