First, the confusing part for marketers: in tech, PR almost never means press relations. It means pull request.
A pull request is how changes get into a codebase safely. Instead of editing the live project directly, you prepare your changes on the side, then open a PR on GitHub that says: here is what I want to change, and why. Someone reviews it, comments on it, asks for adjustments, and when it looks good, merges it in. Think of it as a tracked-changes document sent for approval, but for code.
Why you keep hearing it
Because PRs are where AI coding work meets human judgment. AI agents increasingly do programming tasks, and the standard way they deliver their work is by opening a PR. "The agent opened a PR" means the AI finished a task and packaged the changes for a human to review before anything goes live.
What it means for you
The PR is the safety step. When people debate whether AI can be trusted to write software, much of the practical answer lives here: the AI proposes, a human reviews, and nothing ships without approval. If you are ever in a meeting where "PRs" fly around, mentally substitute "proposed changes awaiting review" and the sentence will usually make sense.