A DAC is a Digital to Analogue Converter. It takes a digital signals, comprising a code of 1's and 0's, and converts that into an audio waveform which can then be sent to the output device (speaker/headphone etc. ) which is by nature analogue.
Anything that takes digital audio and outputs an analogue signal has one or more DAC's somewhere in the chain. Your computer's inbuilt audio capabilities include a DAC, however it is not of particularly high quality. Simplistically, the quality of a DAC is measured by how accuractely it converts the digital data it receieves into an analogue waveform - low quality DAC's introduce harmonic distortion and frequency response aberrations, as well as jitter (when the digital data doesn't arrive quite on time, thereby producing slight compressions and rarefactions in the shape of the waveform as the time axis of the wave form is no longer exactly accurate).
There are various ways to add a better external DAC to your computer, as well as a better internal one in the form of a better sound card. To take the extrnal route, for maximum simplicity you want something with a USB interface so that you can simply use the USB port of your computer to output the digital audio. If you have optical or coaxial out, that will also output digitally to the external DAC. That DAC will then have analogue outputs which you can connect to your headphone/speaker amplifier/s.
