There are several islands that are collectively called the "Galapagos," and are located offshore of mainland Ecuador. It's a short flight from Quito or Guayaquil, the two major cities in Ecuador. Once on the islands, you can board a cruise ship, or you can go "island-hopping," which means you spend each night on the islands in hotels, and take short hopper flights to different island during the day. Galapagos Cruises are more popular, but island-hopping is a great alternative, especially if you are prone to sea-sickness.
On each island, you'll meet different animals, birds, and landscapes. You may spot finches, iguanas, seals, sea lions, dolphins, a variety of fish, hawks, albatross, even penguins. But perhaps the most intriguing of all are the giant Galapagos tortoises.