Why it matters when you are writing
The appeal is speed and priority. Journal review can take a year; a preprint is public in days, establishes when you made a claim, and can be cited and built on while the manuscript is under review. In physics, mathematics, and computer science this has been standard for decades, and in the life sciences it is now normal. In parts of the humanities and in clinical medicine it remains contested.
Citing one is straightforward as long as you are explicit. Every major style has you name the server and mark the status — APA puts the label in brackets, and the reference points to the preprint DOI. Two obligations follow: say in your prose that the source is a preprint when the claim is load-bearing, and check before submission whether a peer-reviewed version now exists. If it does, cite that instead, because the numbers may have changed.
Read a preprint the way a reviewer would, since nobody else has. Look at the methods and the sample before the abstract’s conclusion, and treat a striking result with more caution than you would in a reviewed journal. Some servers post reader comments and version histories, which are genuinely useful — a v3 that quietly revised an effect size tells you something the v1 headline did not.