The church of San Rufino, when compared to other Italian churches, and even just to the other churches in Assisi, is not inherently very interesting. The exterior and the interior both bare features identifying San Rufino as an Umbrian hill town church, and consequently, it doesn’t stick out much.
Two other churches stood on the site before the present one was built, and even before those two, a Roman cistern was built beneath where the bell tower currently stands. You can visit the cistern if you're so inclined. The church also houses a little museum where you can view a series of frescoes, some relics, and pieces from the original church. Again, this is not unlike any number of other Italian churches.
But there is something that makes this place exceptionally unique. The main reason to visit this relatively small, unassuming church is its baptismal font. Once upon a time, baby St. Francis, baby St. Clare, and baby Emperor Frederick II were all baptized here. And while that gives the church itself historical significance and a great deal of interest for pilgrims, the actual baptismal font is also still present (and still used), so you can stand in the same spot where their parents or a priest once held them. In Assisi, it is always fascinating to consider the significant individuals who have walked through its narrow streets, but standing by the font, envisioning each of these three individuals as squirmy babies with entire lifetimes of influence ahead of them, is a genuinely powerful experience.