What is a DAC, and do you actually need one?
A digital-to-analogue converter turns the digital audio file into the analogue voltage a speaker or headphone needs. Every device that plays audio already contains one — so the question is never whether you need a DAC, but whether the one you have is the limiting factor. Usually it is not.
What the chain actually is: the file is decoded, the DAC converts it to an analogue signal, and an amplifier raises that signal to drive the transducer. When people buy "a DAC" they are almost always buying a combined DAC and headphone amplifier, and the amplifier is generally doing the useful work.
Where an external unit genuinely helps:
Hard-to-drive headphones. High-impedance or low-sensitivity headphones need more voltage than a phone or laptop output can supply. Underpowered, they sound thin and lack bass — and this is the one case where the improvement is unmistakable.
A noisy output. Laptops and desktops frequently have audible interference — hiss, or whine that changes when you move the mouse. Moving conversion outside the computer removes it entirely.
No headphone jack, where a small dongle is simply the connector.
Specific connectivity — balanced outputs, optical input, multiple sources.
Where the benefit is minimal:
Modern integrated DACs are very good. Measured performance of the converter in a recent phone or laptop is typically far beyond the threshold of audibility, and the differences between competent converters are extremely small.
Easy-to-drive headphones and earbuds are already being driven adequately.
Bluetooth, where the conversion happens in the headphones and an external DAC does nothing at all — a common and expensive misunderstanding.
Hi-res files, where the format matters less than the recording and the transducer.
The honest priority order for spending: headphones or speakers first, by an enormous margin; then room treatment or fit; then amplification if your headphones demand it; then conversion.
Specifications to ignore mostly: sample rate support beyond what you play, and chip names used as marketing.