Annual means that the plant has a full life cycle (seed-to-seed cycle) in at most one year. It will germinate, bloom and die that year. This is not a calendar year per se. Some species germinate in autumn, survive through the winter and bloom next spring. A good example is the French Marigold.
A biennial plant takes two years to complete it's life cycle. It will germinate and grow, survive through one winter, and in the second year it will grow more, bloom, and die. Biennials are less common than both annuals and perennials. A well-known example is parsley.
Perennials are plants that live more than two years. By this definition, many plants including trees are perennial, although the term is more commonly used for herbaceous plants. A good example is a shasta daisy