Round green shiny leaves 2inches in diameter dark red on back of leaves
Hi Liz, these are some of my favorite little plants; although they're not actually a succulent plant, they do have succulent leaves! This is a type of Begonia, which go by the same name as a common name.
These are often grown as indoor houseplants in combination with ferns and African violets, because they thrive in those kinds of conditions; high humidity, constantly damp soil, and bright filtered light.
Many different kinds can be found; the Rex begonias are incredibly marked with complex patterns, and these are grown more for the foliage. Others can be found planted in hanging baskets to display under a covered porch, out of the sun. Many more have been developed for bedding plants, and your little guy seems to be one of those.
Interestingly, these are one of the few plants that can be rooted by a leaf; although many succulent plants such as Echeveria have this trait, there aren't a lot of other types of plants that can be propagated this way.
Take a leaf with a bit of stem still attached and place it in a pot of sterilized potting soil. New roots and a tiny plant will emerge in time.
Watch out, Begonias can be equally as addictive as succulents; pretty soon you'll have a collection of hundreds of different ones, each unique and beautiful.