Wear the trousers
Be in charge.
An old English folk tale has it that parsley grows best in a household where the wife wears the trousers.
To be 'wearing the trousers' is to be the dominant member of a household. In the days that this phrase was coined that person was normally expected to be the husband and father. The only reason to employ the phrase at all was to relate it to a woman, with the implication that the normal order had been overturned and that a woman was dominant over her husband.
The phrase was known in the USA from the late 19th century. It probably originated there as printed reference to it elsewhere don't appear until well into the 20th century. The Manitoba Daily Free Press used the term in November 1880, in an article about the domestic life of White Indians and their squaws - who we would now call Native Americans:
"The squaws are very beautiful and are as fond of ornaments as Indian women usually are. The women are called ladies and they sometimes wear the trousers or boss the white Indians, their husbands."
It may seem odd that 'wearing the trousers' is first found in America as 'trousers' there are now called 'pants'. Pre-19th century both the USA and Britain referred to close fitting breeches as pantaloons. These were sometimes worn with loose fitting overgarments. In the mid 19th century in the USA these overgarments began to be called pants. In the UK pantaloons became pants and the overgarments trousers.
It may be that 'wearing the trousers' is a variant of 'wearing the pants' as this also is found in US sources around the same time, as in this example from the New York Times in February 1898:
Women will not shy at mice,
By and by,
When they get the coming chance
They will march in the advance,
And may even wear the pants,
By and by.
See other phrases that were coined in the USA.