c. 1400 as a term in astronomy, "angular distance of a star below the horizon," from Old French depression (14c.) and directly from Medieval Latin depressionem (nominative depressio), noun of action from past participle stem of Latin deprimere "to press down, depress" (see depress).
The literal sense "act of pressing down, state of being pressed down" is attested from 1650s. The meaning "dejection, state of sadness, a sinking of the spirits" is from early 15c. (as a clinical term in psychology, from 1905); meteorological sense is from 1881 (in reference to barometric pressure); meaning "a lowering or reduction in economic activity" was in use by 1826; given a specific application (with capital D-) by 1934 to the one that began worldwide in 1929. For "melancholy, depression" an Old English word was grevoushede.
A melancholy leading to desperation, and known to theologians under the name of 'acedia,' was not uncommon in monasteries, and most of the recorded instances of medieval suicides in Catholicism were by monks. [Lecky, "History of European Morals"]
Old English great "big, tall, thick, stout, massive; coarse," from West Germanic *grauta- "coarse, thick" (source also of Old Saxon grot, Old Frisian grat, Dutch groot, German groß "great"). If the original sense was "coarse," it is perhaps from PIE root *ghreu- "to rub, grind," via the notion of "coarse grain," then "coarse," then "great;" but "the connextion is not free from difficulty" [OED].
It took over much of the sense of Middle English mickle, and itself now is largely superseded by big and large except in reference to non-material things. In the sense of "excellent, wonderful" great is attested from 1848.
Great White Way "Broadway in New York City" is from 1901, in reference to brilliant street illumination. The Great Lakes of North America so called by 1726, perhaps 1690s. Great Spirit "high deity of the North American Indians," 1703, originally translates Ojibwa kitchi manitou. The Great War originally (1887) referred to the Napoleonic Wars, later (1914) to what we now call World War I (see world).
"The Great War" — as, until the fall of France, the British continued to call the First World War in order to avoid admitting to themselves that they were now again engaged in a war of the same magnitude. [Arnold Toynbee, "Experiences," 1969]
Also formerly with a verb form, Old English greatian "to become enlarged," Middle English greaten "to become larger, increase, grow; become visibly pregnant," which became archaic after 17c.
"mental condition characterized by great depression, sluggishness, and aversion to mental action," 1690s, from Modern Latin melancholia (see melancholy).