Sonata form is a style of composition which describes the structure of an individual movement in a sonata, a symphony, a concerto, a string quartet and many other works from the middle of the eighteenth century. It is used in a sonata, but it is not the whole Sonata.
Sonata form has three parts or sections, however this form is unlikely to be related to ternary form as the final section is not contrasting but rather the original section with a little modification. It can therefore be considered to be rounded binary form.
Exposition: The initial introduction of the theme. The composer allows the listener to be exposed to the first theme or musical idea for this piece. Development: This section takes the initial theme and develops it in different ways.
Recapitulation: The composer uses this section to refresh the listeners memory and repeats the original idea with slight improvements that often come from the development section.
Now to look at these parts in a little more detail.
The exposition consists of two themes called subjects which contrast with each other.
First subject: In the tonic key, rhythmical in character.
Transition: Joins the sections, can be seen as a merging of the old into the new
Second subject: In the key of the dominant or a related key.
A contrasting idea in tonality, texture or rhythm.
Often more melodic and longer than the first subject.
Coda: Referencing the first subject this section concludes the exposition.
The development section is an area where the composer plays with the two themes. They are reworked, compressed, extended, inverted or transposed. Words that you can used to describe this sections movements are as follows
The composer combines the themes and weaves the concepts together developing many variations until a form of conclusion is reached.
The recapitulation is the restatement of the themes from the exposition with some variations to add interests and variety. These additions can be melodic or may use ornamentation. Musical devices may be used to the connect themes in a transition period. Often the second subject is represented in the tonic key as opposed to the original dominant. As before this section ends in a coda which concludes the piece.