The time that something is due (bordering on overdue) to be done.
For example, "It's beginning to get dark. It's high time we got started on putting up the tent".
This is distinct from the similar 'a high time', meaning 'a happy and jolly time'.
For example, "the party went really well. A high time was had by all".
This phrase has also been used to mean 'a heated argument', but that meaning is unused and archaic now.
Origin (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:
ANTIPHOLUS OF SYRACUSE:
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
Doth for a wife abhor. But her fair sister,
Possess'd with such a gentle sovereign grace,
Of such enchanting presence and discourse,
Hath almost made me traitor to myself:
But, lest myself be guilty to self-wrong,
I'll stop mine ears against the mermaid's song.
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."
See other phrases and sayings from Shakespeare.