His role in the relationship is to be her sugar daddy and provide her with power and material wealth. Hers, beyond providing sex, is to remind others that he is powerful or rich enough to be desirable to such a woman despite his age and thus to serve as a marker of this status -- hence the "trophy" part. A specialized type of gold digger.
Those women are usually at home, 24-hour luxury, and with the children. Sun-bathing, rich friends socializing, -just enjoying the wealth and producing his children are her job.
Ginger McKenna from the 1995 film Casino is another.
Oh, we're still so young, desperate for attention
I aim to be, your eyes, trophy boys, trophy wives