In the simplest terms, a perennial is a plant that lives for at least 3 or more years. We usually use this term to describe herbaceous perennials when talking about gardens. Trees and shrubs last for many years too of course, but these are woody plants. The life span of a perennial varies quite a bit, depending on climate, soil conditions, insects or diseases and the particular plant in question.
Annuals are plants that complete their life cycle within one year. Examples: marigolds, petunias, impatiens and zinnias.
Biennials are plants that usually need two years to bloom, set seed and die. Sometimes they get mixed up and take one year or even three years to complete this cycle. Examples: sweet william, forget-me-not, foxglove, lupines and canterbury bells.