Imagine you have a big bowl of gelatin dessert or jello. You stick your finger in the middle of the bowl and start moving it around in a spiral motion. The middle of the bowl stays relatively flat, but as you move your finger towards the edges, the gelatin starts to twist and curve in ways that look pretty cool.
That's basically what a Roman surface is, but with math instead of gelatin. It's a type of geometric shape that twists and curves in interesting ways, but always stays connected in one piece - kind of like a wavy piece of ribbon.
The Roman surface was first studied by mathematicians in ancient Rome (hence the name) and has been used in many different branches of math and science since then. It's also just really fun to look at and play around with!