Binary form is a way of structuring a piece of music.
A piece in binary form will be in two halves, usually roughly equal in length. The first half will start in a certain key, and end in a different key. If the key at the start was a major one, the key at the end of the first part will generally be the dominant of it (a fifth above), so that a piece beginning in C major will end the first half in G major. If the starting key is minor, the music will generally move to its relative major key, so if a piece starts in C minor, it will end the first half in E flat major. The first half is often repeated.
The second half of the piece begins in the key that the first half ended in, and ends in the original key of the piece. The second half may also be repeated.
Binary form is sometimes characterised as having the form AB, although AA' is also frequently used. This second designation points to the fact that there is no great change in character between the two halves. The rhythms and melodic figures used will generally be closely related in each half, and if the piece is written for a musical ensemble, the instrumentation will generally be the same for both halves. The contrast between the two halves is purely one of the keys used.
Binary form was popular in the Baroque period, often used to structure movements from sonatas for keyboard instruments. It was also used for short one movement works. However, around the middle of the 18th century, the form largely fell from use as sonata form, which has similarities to binary form, was developed. When it is found in later works, it is usually as the form of the theme in a set of variations.