This is a very good question and very important to know the difference if you are expecting them to grow at certain times of the year.

 Annuals last one season.  Flowers like petunias and marigolds are popular annuals.  They generally will bloom profusely, especially if you remove the dead flowers.  They will generally die off with the first frost.  You will have to replant new plants each spring although some may sprout from seed dropped by the plants.  You will want to confirm the cold tolerance of the plant you are choosing with the coldness zone you are living in.  Plants may sometimes be referred to as hardy, half-hardy, or tender for their cold tolerance.  Hardy plants would be able to handle several degrees of freezing temperatures.  Half-Hardy plants are midway between hardy and tender.  Most annuals are in this range.  Tender plants can't survive in any degree of frost.  These would be best planted late spring, they do their best in tropical or subtropical climates.

Biennials grow in two seasons.  They work on growing their leaves and building up strength the first year.  The second year you'll see them flower, set seed and then die.  Examples would be Foxglove and Hollyhocks.

 Perennials will generally last for more than two seasons.  How long they will live varies by plant.  Some seem to live for decades, others may last only two to three seasons.  Usually, the foliage dies back each season although some have an evergreen foliage that will last through the winter.  There are many choices but some favorites are Daylily, Aster, Hosta, Weigela, Phlox and many decorative grasses like Fountain grass or Dwarf Variegated Ribbon grass.

 It's a lot of fun to plant a garden with all of these different types.  If you do, you will enjoy the variety and have something growing at all times.