The Original Four
Jebediah is one of the original four kerbonauts, along with Bill, Bob, and Valentina who wear the orange jump suits instead of the customary grey ones. He is the only default male kerbal with the attribute badS = True. Short for "badass", this makes Jeb's facial expression and general reaction be "happy" ones in almost all situations which might trigger "afraid" reactions in the typical kerbonaut. Whatever effect his dead-middle ratings for Courage and Stupidity would have on personality are overridden by his sheer badassery. Valentina Kerman is often considered a female equivalent to Jebediah Kerman and also has the badS = True attribute, the two are the only default kerbals with the badS flag.

Fame
For several reasons, Jebediah "Jeb" Kerman is the most well-known character from KSP (though it's possible Kerbals themselves consider Wernher von Kerman more famous).

Since Jeb is always first on the list of kerbonauts, he will by default be the first kerbonaut to board any vessel launched. In some cases, even after removing Jeb from the crew assignment of a vehicle in the VAB or SPH, if the Crew tab is left before launching, Jeb will again be aboard – sometimes the only kerbonaut aboard.

As with all of the original four he will re-spawn if he goes MIA (missing in action due to exceeding the 2.5km load distance in an atmosphere) or KIA (killed in action), this means that unless Jeb is stranded the player will constantly get Jeb for flights.

In an official loading artwork by Squad, Jeb appears to be holding hands with Valentina, identified with their orange veteran suits, leading to the theory that they are in a relationship. Upon closer inspection, however, they may just be bumping their fists (most likely).

All told, the odds of having Jeb on any particular flight are far higher than any other kerbonaut. KSP players are likely to have Jeb along for all the "firsts" of their space program and have many of their flights with Jeb as their pilot, assuming they don't launch him into deep space on spent fuel tanks before learning to orbit properly. Jeb appears in many gameplay videos for the same reason.

The developers additionally highlight Jebediah, featuring him in some of the training scenarios. Jeb is in KSP comparable to Mario. He is the namesake of many Kerbal Space Program related components like MechJeb or the RoboJeb bot in this wiki.