When you look at a mirror, the light is reflected back in parallel lines so you see a perfect reflection.
When you look at the back of a spoon, the light is reflected and spread out so your reflection is warped to look bigger.
When you look at the front or inside of a spoon, the light is reflected opposite of how the back reflects the light. It isn't spread out, but focused at a point just a bit above the rom of the spoon. When it reaches your eye, the light has passed by the focal point and is spreading out again. But, because your passed the focal point, the reflected light from the bottom of the spoon is now at the top. The light that hit the top of the spoon is reflected, passes through the focal point, and carries on, now at the bottom of the reflected image.
It's basically because of that focal point. If you could get close enough you'd pass through that point and see an upright image again. Try it with a large, metal mixing bowl.