A DAC is a Digital to Analog Converter. It coverts those 1's and 0's stored on digital media like a CD to the analog signal that your headphones / speakers require. A headphone / speaker cannot properly handle and will sometimes be damaged by a digital signal.
A typical audio train would be:
CD player --->External DAC ( Output will be analog ) ---> Amp ( higher amplitude analog signal ) ---> Speakers / Headphones
Other than the conversion process from digital to analog a DAC is also responsible for controller a lot of the noise in a system. A good DAC will suppress noise from motors, fans, computer mice, and other internal workings. A bad DAC may sound noisy with hiss/hum, or even start to blur the sound.
Hope that helps.
If you can plug you headphones / speakers into a CD player then the CD player has a DAC in it.