A trophy wife refers to a marriage pattern in Western society in which some men marry attractive women as a form of display intended to exhibit their wealth and success to others.
Often rich and successful men who follow this pattern divorce their first wives, often with a generous divorce settlement, and then marry a second much younger woman. In many cases this pattern is repeated with subsequent wives. This marriage pattern is of interest to anthropologists because is can be seen as a form of serial polygamy and is analogous to patterns of polygamy in other societies.
Motivation of men who follow this pattern
The primary motivation of men who follow this pattern is in order to impress others. The man is considered well endowed or more manly if his wife is more attractive. So when she gets older and less attractive the man might divorce her and remarry a younger, more attractive woman.
Motivations of women to become trophy wives
The motivation for women to become trophy wives is usually either money or the man's physical attractiveness. Or sometimes she won't even know she is a trophy wife. When it is for money it is because the man is wealthy. If it is because he is attractive it is usually to impress friends.