Rounded binary form is a slight variation on the simple binary. The variation is found in the fact that the second section states a new musical idea "B" and then returns to the first idea "A." The diagram of this form would be A - (B A) as opposed to the typical A-B of a regular binary form.
Some people may think of this as ternary (3 part) form (A-B-A), but there are several differences between a true ternary and a rounded binary form. First, the "B" section of a true ternary form dramatically contrasts the musical statement of the "A" section. In rounded binary, the "B" section can have similar musical attributes to the "A" section. Second, the return of "A" in rounded binary is usually abbreviated (half of the original statement). In true ternary form the return of "A" is a complete restatement of the section.
The "B" section of a rounded binary form usually moves to a new (temporary) key center. Pieces that are in a major key often move to the key a fifth above (the dominant) for this temporary key center. Pieces that are in a minor key often move to the relative major. Another technique composers use in the "B" section is fortspinnung. This is a German term for a sequence of intervallic changes that take a musical motif through a process of development. The "B" section usually ends with a dominant harmony of the original key which leads back to the tonic for the repeat of "A." The picture below is a slide from the my Learning Music With Ray video on rounded binary form. It shows an original composition which is an example of rounded binary.