push (v.)

c. 1300, pushen, "to shove, move onward, strike with a thrusting motion, thrust forcibly against for the purpose of impelling," from Old French poulser (Modern French pousser), from Latin pulsare "to beat, strike, push," frequentative of pellere (past participle pulsus) "to push, drive, beat" (from PIE root *pel- (5) "to thrust, strike, drive").

Transitive meaning "urge, incite, press" is by 1570s; that of "promote, advance or extend by persistence or diligent effort" is from 1714; intransitive sense of "make one's way with force and persistence (against obstacles, etc.)" is by 1718. The meaning "approach a certain age" is from 1937. For palatization of -s-, OED compares brush (n.1); quash. Related: Pushed; pushing.

To push up daisies "be dead and buried" is from World War I, but variants with the same meaning date back to 1842.

"Pushing up the daisies now," said a soldier of his dead comrade. [The American Florist, vol. xlviii, March 31, 1917]

To push (someone) around "bully, browbeat, domineer" is by 1923. To push (one's) luck is from 1754. To push the envelope in the figurative sense is by late 1980s.

push (n.)

1560s, "a driving or impelling thrust," from push (v.). By 1590s as "a vigorous attempt." By 1803 as "a determined advance, a pushing forward." The sense of "persevering enterprise, a determined effort to get on" especially if inconsiderate of others is by 1855. Phrase when push comes to shove "when action must back up threats" is by 1936. An earlier Middle English noun push "a pustule, pimple, boil" probably is from pus by influence of push.

Definitions of push
push (v.)
move with force;
He pushed the table into a corner
Synonyms: force
push (v.)
press, drive, or impel (someone) to action or completion of an action;
He pushed her to finish her doctorate
Synonyms: bear on
push (v.)
make publicity for; try to sell (a product);
The salesman is aggressively pushing the new computer model
Synonyms: advertise / advertize / promote
push (v.)
strive and make an effort to reach a goal;
We have to push a little to make the deadline!
Synonyms: tug / labor / labour / drive
push (v.)
press against forcefully without moving;
she pushed against the wall with all her strength
push (v.)
approach a certain age or speed;
She is pushing fifty
Synonyms: crowd
push (v.)
exert oneself continuously, vigorously, or obtrusively to gain an end or engage in a crusade for a certain cause or person; be an advocate for;
The liberal party pushed for reforms
The Dean is pushing for his favorite candidate
Synonyms: crusade / fight / press / campaign / agitate
push (v.)
sell or promote the sale of (illegal goods such as drugs);
The guy hanging around the school is pushing drugs
push (v.)
move strenuously and with effort;
The crowd pushed forward
push (v.)
make strenuous pushing movements during birth to expel the baby;
`Now push hard,' said the doctor to the woman
Synonyms: press
push (n.)
the act of applying force in order to move something away;
he gave the door a hard push
the pushing is good exercise
Synonyms: pushing
push (n.)
the force used in pushing;
the push of the water on the walls of the tank
Synonyms: thrust
push (n.)
enterprising or ambitious drive;
Synonyms: energy / get-up-and-go
push (n.)
an electrical switch operated by pressing;
the elevator was operated by push buttons
the push beside the bed operated a buzzer at the desk
Synonyms: push button / button
push (n.)
an effort to advance;
the army made a push toward the sea