DAC stands for digital to analogue converter. Essentially it does what onboard audio and sound cards do, convert digital audio data into an analogue signal, which is then sent to the amplifier, then the speakers.
Onboard audio in the majority of cases is pretty basic. It does the job, but depending on what you connect to it, can either be good enough or lacking a bit. In most cases a budget sound card will be a decent improvement.
A DAC is a sound card if you like, without all the other bells and whistles that go with a sound card. No 5.1, no sound effects, etc, just good conversion from digital to stereo analogue.
If the speakers or headphones are of good enough quality, then a DAC may be worth getting. For cheaper speakers and headphones or headsets, a budget sound card will be more than good enough.
With £100 to spend, I'd spend no more than £20-£25 on a Xonar DGX, then the rest on the speakers, or ideally spend as much as you can on the speakers, then get a sound card when possible. While it's good to have a nice sound card or DAC, the quality of the speakers is far more important. Onboard audio will suffice until a decent sound card or DAC can be afforded, but if you skimp on the speakers just to be able to get a sound card or DAC at the same time, then you're stuck with them.