Meanings
Uncertain; OED (3rd edition 2007) says that the origin of the phrase is unknown and states that a common suggestion is that the phrase originates with the distinction of the minuscule letters p and q in either the school-room or the printing-office, but goes on to say that the chronology of the senses argues against this since no such connotation is evident in the earliest quotations.[1]
How to pronounce "mind one's ps and qs":
AU
To be very careful to behave correctly.
Example: "When we go to visit, do remember to mind your ps and qs, children – we don't want another incident like last time."