Proselytize comes from the noun proselyte (meaning "a new convert"), which comes from the Late Latin noun proselytus.

What is it called when you try to convert someone to your religion?

To proselytize is to try to persuade someone to switch to your religious beliefs or your way of living.

What is an example of proselytizing?

Proselytize is to preach your religion or beliefs especially to convert others, or to promote a certain course of action. An example of proselytize is when you explain Christian theology to try to convince your Agnostic friend to join the Christian faith. To attempt to convert someone to one's own religious faith.