To visit someone, usually for a specific purpose. I will call on my grandmother this weekend to see how she's doing.
To ask someone to do something, especially in a formal or official way. The teacher called on the students to submit their assignments by Friday.
To appeal to someone for help or support. The charity called on the community to donate to the relief fund.
To select or choose someone to speak or answer a question. During the meeting, the chairperson called on Sarah to present her report.