Solicit means to ask for. It is what those people on the street are doing, when they ask, "Do you have a moment to talk about the destruction of the planet?" They are soliciting donations for their cause.
Solicit has an official sounding impressiveness to it––doesn't soliciting donations sound better than begging for money? It can also have a more sinister cast. "When the teacher left the room, two girls solicited their friends to throw all the textbooks out the windows, injuring members of the cheer squad below — where they were soliciting signatures for a petition banning smoking in the football locker rooms."