High TIme - Double Meaning
We normally think of this phrase as meaning that "Now" is the time to do something. An example might be, "We are almost out of black ink. It's high time we got some more on order."
This phrase has also been used to mean 'a heated argument', but that meaning is unused and archaic now.
The origin of "High Time"
'High time' derives from the allusion to the warmest time of day - when the sun is highest in the sky. High noon is another way of saying it. Shakespeare used it in his Comedy of Errors, 1590:
There's none but witches do inhabit here;
And therefore 'tis high time that I were hence.
She that doth call me husband, even my soul
Origin "A High Time"
'High times' comes from the same root as 'high days and holidays', i.e. days of religious note and festivals. High in that sense has been used in English since the middle ages, although there are few references to it in print until the 19th century, as in this from the Canadian newspaper, The British Colonist, 1858:
"The Johns had a high time, drinking brandy and eating fried hog."