Kukulkan's probe was a "mysterious alien space probe" that was sent out by Kukulkan that possessed a highly advanced propulsion system.
In 2270, the probe approached the Federation homeworlds, made a scan of Earth's system, and then sent a signal out into space. Before it could be intercepted, it self-destructed.
Following the incident, the USS Enterprise followed the trail of disrupted matter left behind by the probe, where they eventually encountered Kukulkan's ship. (TAS: "How Sharper Than a Serpent's Tooth")