Can you help me understand what exactly a DAC does?
I don't see that anyone has answered this yet for you. I will try to do this at a simplified/high level, and we can take a deeper dive if you like.
Sound is an analog waveform, so if source material is not already analog (vinyl, tape, legacy OTA Am/fm) then somewhere between the digital source and the speakers /transducers there must be a conversion from digital to analog - hence the Digital to Analog Converter (DAC)
A preamplifier or pre amp or pre is literally something in the chain before (pre) amplification (boosting) of the analog waveforms from so called line level (low) to so called speaker level (high) signal amplitude. The pre function is largely two-fold: it switches between multiple sources, and provides a volume control.
Since you have a TT, you also need a function performed by a phono preamp or so called phono stage. The signal produced by the cartridge/needle is extremely small, and itself must be boosted just to get to line level required by the preamp. Also, when the record grooves are cut, the low levels have been reduced because of cutting head issues, and the highs have been emphasized, all according to a standard protocol set as the so called Recording Industry Association of America (RIAA) curve. So the phono pre applies the inverse of that Emphasis/de-emphasis boosting the lows and cutting the highs by applying the so called RIAA equalization curve, returning what is then a flat frequency response in a line level signal ready for the preamp and amp.
So, now you need box(es) to perform those functions, which could be three separate single function device, or those functions could be combined in any combination in one or more multi-function box(es).
Sorry it got a little long, hopefully still easy to follow.