It's not an article, but Nick Bostrom's talk on humanity's biggest problems was what made transhumanism "click" for me. He discusses defeating death, mitigating existential risk, and the potential benefits of cognitive enhancement (as well as transhumanist values in general).
Another good introduction is Three Major Singularity Schools, but that's not on LW either.
ETA: If your main goal is to show off LessWrong rather than provide a good introduction to transhumanism, then just link to the about page.
Summary: if you could show a page of LW to a random student who was interested in science, but couldn't otherwise communicate with them, which page would you choose?
The Oxford University Transhumanist Society is a student society who arrange speakers on transhumanist topics - ranging from cognitive enhancement to AI to longevity to high-impact careers to Xrisk to brain-machine interfaces. The audience is a mixture of undergraduate and graduate students, mostly scientists, who are interested in the future of science and technology, but by no means self-describe as transhumanists.
This week we're finally getting organised and producing membership cards. We intend to put a URL in a QR code on them, because people expect cool techy stuff from the Transhumanist society. It'd be nice if the link was something slightly more imaginative than just H+ or the facebook page. Naturally, I thought it should point to LW; but where specifically? The About page, a very good article from the Sequences, something from Eliezer's website, MoR...? A well chosen page, showcasing what LW has to offer, could well draw someone into LW.
Suggestions welcome. One article (or very similar set of articles) per top-level comment please, so people can upvote suggestions in a targetted manner.