The public release of the draft of a research paper claiming that P ≠ NP is potentially big news indeed. This has caused quite a discussion on Hacker News, and I for one certianly look forward to the professional consensus on this paper after it's been released and subject to rigorous peer review.
Most people outside of the Computer Science field will probably say, "Why should I care?"
The topic is close to some people's hearts, and if you foresee an interaction with such people, it pays to have some ammunition to take your conversations to the next level.
You don't need to know too much. Just enough to a ask one more question. One more intelligent question to distinguish yourself from the mass of blaberring coconuts. Then stop and listen. More often than not, I find myself gaining new insights into the topic, but more importantly, gaining new respect from the person.