The phrase originates from gender roles where traditionally men had the power. Even though it's the 21st century, in their house, he still wears the trousers.
Pro Tip 2/3
Cultural Nuance
It's a British expression, so be mindful that it may not be understood globally. While working with American clients, she avoided saying 'wear the trousers'.
Pro Tip 3/3
Informal Context
Suitable for casual conversation, but may be inappropriate in formal settings. At the family dinner, Uncle Joe joked that Aunt May wears the trousers.