This is the 11839th most frequent Russian word.
замуж
"Замуж" means "to get married" (for a woman).
The word "замуж" is used here to indicate the aspiration of a female person to enter into marriage.
Она мечтает выйти замуж за принца.
She dreams of marrying a prince.
In this example, "замуж" is part of the phrase "выйти замуж", which refers to the act of a woman entering into marriage.
После университета она вышла замуж за своего одноклассника.
After university, she got married to her classmate.
Here, "замуж" is used in the negative form "не планирует выходить замуж", indicating the decision not to enter into marriage at a specified time.