What is the Sonata Form?

Sonata form (also sonata-allegro form or first movement form) is a musical structure consisting of three main sections: an exposition, a development, and a recapitulation. It has been used widely since the middle of the 18th century (the early Classical period).  It was more of a general convention to adhere to (and often manipulate) rather than a strict form with rules.

The Typical First Movement of symphonies, string quartets, sonatas (and more) had three main sections  (the "Sonata Form"):

     1.  Exposition  -  Typically it states the two themes, often in two different keys:

         The first theme (known as das Thema) is in the key of the composition's primary key.  

         The second theme is then introduced, usually in a different key than the first. 

          (in some works the exposition is repeated before going on to the development section) 

     2.  Development  -  Next, the two themes are used in variations to create the real "excitement"

                                      of the movement.  This is where the composer shows off his creativity.

     3.  Recapitulation  -  Then the first two themes are replayed, usually with harmonic

                                         variations to keep them interesting.

       Optionally: 

              1.  There could be a coda ("tail") where the composer adds something to rap up the

                    end of the movement.  Prior to Beethoven, the coda was usually 20 to 40 seconds long.

              2.  The first movement could have a slow introduction before the Exposition began.
                   Beethoven used an introduction in Symphonies 1, 2, 4, and 7.

More on the sonata form:

While it is typically used in the first movement of multi-movement pieces, it is sometimes used in subsequent movements as well—particularly the final movement.  The teaching of sonata form in music theory rests on a standard definition and a series of hypotheses about the underlying reasons for the durability and variety of the form—a definition that arose in the second quarter of the 19th century.  There is little disagreement that on the largest level, the form consists of three main sections: an exposition, a development, and a recapitulation; however, beneath this general structure, sonata form is difficult to pin down to a single model.