solicit
To ask people for something, usually in a serious way.
To solicit means to ask for something, often in a persistent or formal way. When a charity solicits donations, it reaches out to people asking them to contribute money. When a teacher solicits questions from the class, she's actively asking students to speak up. A business might solicit feedback from its customers to learn how to improve.
The word often carries a sense of seeking something specific from people. Door-to-door salespeople solicit business by knocking on doors and trying to sell products. A politician might solicit votes by asking citizens to support her campaign. When a sign says “No Soliciting,” it means the property owner doesn't want people coming around trying to sell things or collect money.
Solicitation is the noun form. A fundraising letter is a kind of solicitation. So is a request for volunteers or a call for entries in a contest.
The word can have slightly different feelings depending on context. Sometimes it's perfectly normal and professional, like when a newspaper solicits articles from writers. Other times it suggests unwanted persistence, like spam emails soliciting you to buy something you don't need. The key is that soliciting always involves actively seeking something from others, rather than waiting passively for it to come to you.