Scottish engineer William Rankine's 1859 explanation of how curve AC is an adiabatic curve, representing an expansion of a substance made without receiving or emitting heat. [3]
In thermodynamics, adiabatic, from a-, meaning “not”, + -dia-, meaning “through”, + -bainein, meaning “to go” (Waser, 1966), refers to a system undergoing a process in which NO heat is allowed to go through the boundary (e.g. using heat-insulating material); only work is exchanged with the surroundings. [1] The basic model of the term is that in which a substance expands, pushing on the piston, in such a way that no heat transfers across its boundary, whereby all of the energy of the expanding body is transferred to the piston as work (via pressure volume work).

Etymology
The premise of a vessel changing temperature, without the addition of removal of heat, via the contact of a hot or cold body, was first noticed in respect to experiments with the vacuum pump; the following is a synopsis:

Higgins’ theory [1776] accounted for the phenomenon of the heating (or cooling) of a gas when it is suddenly compressed (or expanded): ‘adiabatic’ heating or cooling as it was later called. This had first been noticed in connection with experiments on the air pump. Cullen mentioned it but had no insight into its significance. Higgins also referred to it, and Johann Lambert pointed out that when air enters an evacuated vessel the temperature rises. His explanation was that even ‘empty’ space contains the ‘matter of heat’, so that the entry of air carrying more heat must cause a rise in temperature; and he went on to suggest that suddenly reducing the volume of a void should have a heating effect.”
Donald Cardwell (1971), From Watt to Clausius (pg. 58)

In 1859, William Rankine, in his A Manual of the Steam Engine and Other Prime Movers, introduced the term “adiabatic”, consisting of the double Greek prefixes: a- (not) and dia- (through or across), thus referring to boundaries in which no heat can pass, referring to a special class of pressure-curves corresponding to the case of expansion within an envelope impermeable to heat. [2]

Physical description
In 1936, Italian-born American physicist Enrico Fermi stated that an adiabatic transformation is one that is thermally-insulated and reversible. The "reversible" addendum, however, may not be the the way in which the original sense of the term is used. In any event, Fermi says that in a piston and cylinder, the adiabatic process is done such that the cylinder is made of non-heat-conducting walls and the piston is shifted inward or outward very slowly. [4] The condition of "thermally-insulation" implies that:

$dQ = 0 \,$

Substitution into the first law equation for this process:

$dU = dQ - dW \,$

gives:

$dU = - dW \,$

which means that "adiabatic expansion" correlates to an internal energy decrease; whereas, conversely, "adiabatic contraction" correlates to an internal energy increase.

Quotes
The following are related quotes:

“Suppose a piston moves inward, so that the atoms are slowly compressed into a smaller space. What happens when an atom hits the moving piston? Evidently it picks up speed from the collision. You can try it by bouncing a ping-pong ball from a forward-moving paddle, for example, and you will find that it comes off with more speed than that with which it struck (Special example: V an atom happens to be standing still and the piston his it, it will certainly move.) So the atoms are ‘hotter’ when they come away from the piston than they were before they struck it. Therefore, all the atoms which are in the vessel will have picked up speed. This means that when we compress a gas slowly, the temperature of the gas increases. So, under slow compression, a gas will increase in temperature, and under slow expansion it will decrease in temperature.”
Richard Feynman (1963), Lectures on Physics, Volume One (pgs. 1-4); supposedly an explanation of adiabatic compression on a fundamental level [5]

References
1. Perrot, Pierre. (1998). A to Z of Thermodynamics (adiabatic, pgs. 6-7). Oxford: Oxford University Press.
2. (a) Clausius, Rudolf. (1879). The Mechanical Theory of Heat (pg. 68). London: Macmillan & Co.
(b) Truesdell, Clifford. (1980). The Tragicomical History of Thermodynamics, 1822-1854 (pg. 33). Springer-Verlag.
3. Rankine, William. (1859). Manual of the Steam Engine and Other Prime Movers (adiabatic, pgs. 302, etc.) London: Charles Griffin and Co.
4. Fermi, Enrico. (1936). Thermodynamics (pg. 25). Prentice Hall.
5. Hanlon, Robert. (2020). Block by Block: the Historical and Theoretical Foundations of Thermodynamics (Illustrators: Robert Hanlon and Carly Sanker) (adiabatic, pg. xiii). Oxford University Press.