From The inside story of MCAS: How Boeing’s 737 MAX system gained power and lost safeguards by Dominic Gates and Mike Baker:
During flight tests to certify an airplane, pilots must safely fly an
extreme maneuver, a banked spiral called a wind-up turn that brings
the plane through a stall. While passengers would likely never
experience the maneuver on a normal commercial flight, it could occur
if pilots for some reason needed to execute a steep banking turn.
Engineers determined that on the MAX, the force the pilots feel in the
control column as they execute this maneuver would not smoothly and
continuously increase. Pilots who pull back forcefully on the column —
sometimes called the stick — might suddenly feel a slackening of
resistance. An FAA rule requires that the plane handle with smoothly
changing stick forces.
The lack of smooth feel was caused by the jet’s tendency to pitch up,
influenced by shock waves that form over the wing at high speeds and
the extra lift surface provided by the pods around the MAX's engines,
which are bigger and farther forward on the wing than on previous
Under the proposal, MCAS would trigger in narrow circumstances. It was
designed "to address potentially unacceptable nose-up pitching moment
at high angles of attack at high airspeeds," Boeing told the FAA in a
proprietary System Safety Assessment reviewed by The Times.
Another article from The Seattle Times published in March makes mention of a high speed stall:
Designed to activate automatically only in the extreme flight situation of a high-speed stall, this extra kick downward of the nose would make the plane feel the same to a pilot as the older-model 737s.
This indeed points to a stick-force-per-g test, as @Jimmy mentions in a comment. Since the B737 has a fully irreversible hydraulically actuated flight control system, with an artificial feel that is proportional to dynamic pressure but not to load factor, the obvious mechanism for "lack of smooth force feel" would be having to release the column to some extent due to extra nose-up moment that the aircraft generates.
It is very plausible that the added lifting surfaces from the engine pods create a larger pitch-up moment than the 737NG has in the same circumstances. I'm not really sure how the supercritical airflow over the MAX wing differs from that of the NG to create extra pitch-up.
All of that is the original limited cure for the stick-force-per-g tests. If this was the only thing that needed to be fixed, all would probably have remained well. But the first linked article also mentions:
The flight-test pilots had found another problem: The same lack of smooth stick forces was also occurring in certain low-speed flight conditions. To cover that issue too, engineers decided to expand the scope and power of MCAS.
As you can see, The Seattle Times is my source of information as well...there is no additional information on what were the "certain low-speed flight conditions".