"to urinate, discharge the fluid secreted by the kidneys and stored in the urinary bladder," c. 1300, pissen, from Old French pissier "urinate" (12c.), from Vulgar Latin *pissiare, of imitative origin. To piss away (money, etc.) is from 1948. Related: Pissed; pissing. Pissing while (1550s) once meant "a short time."

He shall not piss my money against the wall; he shall not have my money to spend in liquor. [Grose, "Classical Dictionary of the Vulgar Tongue," 3rd edition, 1796]

To piss money on the walls "throw money around recklessly" is attested from 1540s.

He who once a good name gets,

May piss a bed, and say he sweats.

["Dictionary of Buckish Slang, University Wit and Pickpocket Eloquence," London, 1811] 

"urine," late 14c., from piss (v.). As a pure intensifier (piss-poor, piss-ugly, etc.) it dates from 1940, popularized in World War II. Piss and vinegar "vim, energy" is attested from 1942. Piss-prophet "one who diagnoses diseases by inspection of urine" is attested from 1620s. Piss proud "erect upon awakening" is attested from 1796.

"chamber-pot, earthenware vessel for urine," mid-15c., pisse-pot, from piss + pot (n.1).

1958, intransitive, "go away," chiefly British; the transitive meaning "annoy (someone)" is by 1968, chiefly U.S.; from piss (v.) + off (adv.). Pissed off "angry, fed up" is attested by 1946 (Partridge says 1937); said to have been used in the military in World War II; in common use from 1970s.

"of or pertaining to piss," 1926, from piss (n.) + -y (2). Figurative use as a general term of abuse is by 1972.

1788, "to spray with urine" (trans.), euphemistic abbreviation of piss. Meaning "to urinate" is from 1879. Related: Peed; peeing. Noun meaning "act of urination" is attested by 1902; as "urine" by 1961. Reduplicated form pee-pee is attested by 1923.

well-known plant of the daisy family found in Europe, Asia, and North America, with a tapering, milky root, producing one large, yellow flower, late 14c., a contraction of dent-de-lioun, from Old French dent de lion, literally "lion's tooth" (from its toothed leaves), a translation of Medieval Latin dens leonis. From Latin dens (genitive dentis) "tooth," from PIE root *dent- "tooth" + leonis, genitive of leo "lion" (see lion). 

Other folk names, like tell-time refer to the custom of telling the time by blowing the white seed (the number of puffs required to blow them all off supposedly being the number of the hour), or to the plant's regular opening and closing with daylight. Other names refer to its diuretic qualities (Middle English piss-a-bed, French pissenlit).