An eye agate is an agate that is marked with one or more concentric circles, which look like eyes. The circles are usually a complementary color to the rest of the agate. The eyes are actually little spheres, possibly caused by silicification around a seed crystal of some other material located at the edge of the agate while the rest of the agate is forming. They just look circular because you see their cross-section. Sometimes two eyes will merge, creating a figure-8 inside the stone, as seen in the close-up photo. Eye agates are pretty rare, but they seem to occur more often in agates from Lake Superior and carnelian agates from Botswana.
Lake Superior Agates are a type of agate found near Lake Superior. They were carried across Minnesota by glaciers 10,000 years ago and are so common there that they have been Minnesota’s official state gemstone since 1969. Wisconsin and Michigan have some, too. Lake Superior agates are known for their red color which comes from iron oxide in the surrounding area. Most Lake Superior agates are banded agates, but a few are eye agates, some are “waterwashed” agates (called so because they have been naturally polished by the water on the beach, like sea glass), and, rarest of all, some of them weigh over 2 pounds.
I should also point out that if you ever go looking for agates, the ones in the field won’t be as colorful and they are easy to mistake for other rocks like granite or basalt. Most of the pictures of agates are of nice pretty polished slabs or cabochons, and that tends to give people unrealistic expectations. That’s why the photo shows Lake Superior agates before and after tumbling.
The Minnesota Department of Natural Resources was invaluable in writing this post. More information here: http://www.dnr.state.mn.us/education/geology/digging/agate.html