"walk in a vain, important manner, walk with affected dignity," 1590s, from Middle English strouten "display one's clothes proudly, vainly flaunt fine attire" (late 14c.), earlier "to stick out, protrude, bulge, swell," from Old English strutian "to stand out stiffly, swell or bulge out," from Proto-Germanic *strut- (source also of Danish strutte, German strotzen "to be puffed up, be swelled," German Strauß "fight"), from PIE root *ster- (1) "stiff."
Originally of the air or the attitude; modern sense, focused on the walk, first recorded 1510s. Related: Strutted; strutting. To strut (one's) stuff is first recorded 1926, from strut as the name of a dance popular from c. 1900. The noun meaning "a vain and affectedly dignified manner of walking" is from c. 1600.
of a college or university student, "focus (one's) studies," 1910, American English, from major (n.) in sense of "subject of specialization" (by 1890). Related: Majored; majoring. Earlier as a verb, in Scottish, "to prance about, or walk backwards and forwards with a military air and step" [Jamieson, 1825] a sense derived from the military major.
"walking on the whole sole of the foot" (opposed to digitigrade), 1831, from French plantigrade "walking on the sole of the foot" (1795), from Latin planta "sole of the foot" (from nasalized form of PIE root *plat- "to spread") + gradi "to walk, go, step" (from PIE root *ghredh- "to walk, go"). Used of man and other quadrupeds (bears, etc.) whose heels touch the ground in walking.