Perennials are plants that last for multiple years. Typically, they will grow through the early season, flower, and then die back to their roots. There are many forms of perennials - some grow from bulbs, others have taproots. Some only last for a few years, others may outlive you!
Once established, perennials are usually very easy to care for, and need very little maintenance. Typically they just need a bit of water in their first summer, and then will last for years!