A plant that completes its life cycle in one year, or one growing season. Most annuals, obviously, are not going to be woody plants, or very tall. Most annuals are very short, small plants that bloom,pollinate, seed and die very quickly. A good example would be dandelions.
Calling a plant an annual is a little arbitrary, since probably a great deal of plants that normally die at the end of the year could probably survive if they were in a warm enough climate. That is, if they aren't programmed to go through apoptosis after going to seed.