You can use Properties with Getter and Setter when:
You want an attribute to be “read only” (just the getter, not the setter). The property can do as little as returning a private field, but whoever is accessing the class won’t have access to write anything in the field (i.e. won’t break anything in your class).
You want something else to happen when you get or set a value. For instance, you can have a “Color” property in an entity, but when you set it it also sets the Color property of all the entity’s children, etc. A simple field can’t do that.
I’m sure there’s other cases as well, have to go now!