To incise is to carve or cut into something. You might incise your initials into the old oak tree in your backyard.
When you incise something, you carve it, often as a way of decorating it. Your grandfather might incise his beloved walking stick with the shapes of birds and trees, for example. It's more common to see this word in its adjective form, incised, but you can use it to mean "cut into a surface," or even "make a surgical cut." The Latin root is incidere, "to cut into or cut through."