On June 27, while describing Bartok's Concerto for Orchestra, I gave the following in regards to sonata form: "The basic concept of this form is that there are two theme groups (or melodies with variations), played one at a time, and then mixed together (usually in several different keys) in the development section, and then reprised in the recapitulation." For a brief definition, that works well enough. Today, I would like to direct your attention to a famous example of the form: the first movement of Beethoven's Fifth Symphony. (If you search Beethoven's Fifth Symphony in YouTube, you will be able to hear the same version, and more importantly, use the same times to which I refer. It is 7:05 in total length.)
First Theme Group - 0:00 to 0:44
Second Theme Group - 0:44 to 1:21
(All the above is then repeated.)
First Theme Group - 1:21 to 2:05
Second Theme Group - 2:05 to 2:42
Development Section - 2:42 to 4:00
Recapitulation - 4:00 to 7:05
(Note that the first section, i.e. the first and second theme groups is precisely 1:21 in length, both times. This means that the conductor and orchestra kept the tempo perfectly.)
At this point in music history, the different forms used by composers were being stretched and experimented with; this was one of Beethoven's major contributions, among many. In this piece, it is the recapitulation where that fact is most evident.
Of course, the descriptions of form and so forth can be much more technical than what I've provided here, and there is plenty to read and learn about in this area, but my concern here is that listeners grasp the main concept: two contrasting ideas are played separately, then mixed together, and finally, resolved. The listener who can hear sonata form (when it's present) will be able to understand how musical ideas are developed, contrasted, integrated, etc. He or she will also be able to hear much more deeply into the music. Listening: the above of course, but also try some of Beethoven's influences - particularly symphonies by Haydn and Mozart.