This is the 2927th most frequent Russian word.
вступить
"To enter," "to join," or "to step in."
Here, 'вступить' means 'to join' an organization or group.
Я решил вступить в клуб любителей книг.
I decided to join the book lovers' club.
In this context, 'вступить' is used to mean 'to enter into' a formal relationship such as marriage.
Она хочет вступить в брак с ним.
She wants to enter into marriage with him.
'Вступить' here means 'to start' or 'to engage in' an action, specifically initiating interaction.