This is the 4269th most frequent French word.
engage
To commit, involve, or pledge.
The reflexive verb 's'est engagée' denotes someone's involvement or participation in an activity or group.
Elle s'est engagée dans une organisation caritative.
She got involved in a charitable organization.
The verb 'engage' here is used reflexively to express personal willingness and commitment.
Je m'engage à vous aider avec votre projet.
I commit myself to helping you with your project.
The verb 'engage' is used transitively to mean initiating something, in this case, a conversation.