What makes a jet single pilot certified?
According to this blog:

Up until 1977, the FAA required all jets to be operated by two pilots. In ‘77, Cessna was given approval on a single-pilot variant of the Citation I, the Citation I-SP. The aircraft met the 12,500-pound maximum takeoff weight threshold for small aircraft, but that wasn’t the only single-pilot qualification. Cessna also had to convince the FAA that its pilot workload was low enough for one pilot to handle safely.
According to J. Mac McClellan with Flying Mag, in order for an aircraft to qualify for single-pilot certification in the 70s, “you had to have a boom microphone for hands-free communications-somewhat uncommon 30 years ago-and a fully functioning autopilot. There was also the quaint requirement for a transponder ident button to be mounted on the control wheel. In those days, we would ident on almost every controller handoff.”
One of the most important (and obvious) requirements for single-pilot certification of an aircraft is the fact that all gears and controls must be accessible from the left seat. The autopilot must be seamlessly integrated into the airplane’s navigation systems, and it must be functional for every flight operated by one pilot. The aircraft must have hands-free communication, as well. Aside from those concrete requirements, the rest is subjective.
After a series of test flights, the FAA’s test pilots must come to the conclusion that the aircraft is safe for a single pilot to fly. The design of the aircraft’s controls is one of the most important factors, as one pilot must be able to operate the throttle, the yoke, control wheel, and other flight controls easily from the left seat.

So, all of the aircraft's controls must be operable from the left seat, there must be hands-free communication, and an integrated autopilot.
Now, of course, there is also a single-pilot type pilot's certification, which a pilot can obtain to legally fly aircraft which meet all of the requirements above, yet are larger than the 12,500-pound maximum takeoff weight threshold.