When a Christian falls in love with a heathen and they make up an excuse to date them anyways. They will "evangelicalize" to their significant other while they are dating, in hopes that they will understand the gospel.
Jane tried to evangedate Justin but he turned her down as soon as she made him go to church.
Sarah has been evangedating Drew for months, but I doubt he's ever gonna accept Jesus
When an Evangelical Christian dates a non-Evangelical with the express purpose of using the dating relationship as an opportunity to evangelize the non-Evangelical.
Often the term is used as an excuse to the Evangelical community for why the person is dating a non-Christian helping to overcome the strong bias toward dating a fellow Evangelical.