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A piece in binary form uses two related sections of roughly equal duration. Within the first section, the music may modulate or it may not. The second section usually begins in another key and modulates back to the tonic for its close.
Often, the A and B sections are separated by double bars with repeat signs, meaning both sections are to be repeated.

A :||: B
Tonic (à ?)

? à Tonic

Types of Binary Form:
Simple vs. Rounded
If the A and B sections use entirely different themes, we call the form simple binary.
But, when the B section contains a return of the A section’s opening material in the tonic, the form is rounded binary. In this form, we will think of the beginning of the B section as a bridge that moves the music toward a return of the opening material. The bridge often concludes with a half cadence in the original key for maximal tonal clarity.
Sectional vs. Continuous
If the A section ends with an Authentic cadence in the tonic key, we call the form sectional binary. In other words, since the work closes in the tonic at the end of the A section, it does not tonally point to the next section, and as such is sectionally cordoned off. If there is any other type of cadence (I:HC, V:PAC, for instance), we call the form continuous binary. In other words, in a continuous binary form, the A section points to the next section, since its cadence requires some type of later resolution.
Balanced Binary
It is possible to get a sort of “rhyme” between the ends of the A and B sections. This happens when A’s closing cadential material (in the key of the dominant, for instance) returns transposed to the tonic at the end of B. We call this rhyming binary form balanced binary.

“Two Rotation” form: usually called “simple”
The motives of the A section are recycled in the same order in the B section. In other words, the bridge is the same as A’s opening, and the remainder of A’s themes will return as B progresses, eventually modulating back to the tonic. When this happens in conjunction with a rounded binary form, we can imagine the opening motive being stretched through the bridge into the opening’s return.
(NB: This is a Chris White term)