The teacher elicits the answers from his students by asking relevant questions, leading questions, parallel questions and so on. His aim is to make the students think. The student is impressed that the answer was found by himself.
In the case of a lawyer, he elicits the desired reply from the witness by suitably framing his questions. This elicitation is called cross-examination.
A police officer also elicits information from the suspect in his own way. It is called extraction of confession from the unwilling mouth.