If you haven't already done so, you should check out my article on Using Binary Form in Compositions - I'm going to skip some things covered in that article or assume they're understood.

Ternary form is the "other" big traditional musical form.

Binary is | A | B ||

Ternary is | A | B | A ||

So notice there are three "sections" but only two major musical ideas. This is a little confusing because many people think A B C or A A B might also therefore represent Ternary Form, but they don't (we often call them three part or something else to distinguish them).

The best way to describe Ternary form is "home - away - home".

So Binary Form represents "continuation" or a "exploration" or even, an "unfinished story". The parallel is Binary Form is like "driving from home to work" and therefore Ternary form is like "driving from home, to work, and back home again" (remember though, this is not to imply that Binary forms don't return to the Home key, they do, they just don't use the same home-key material they began with to do so - it's like you leave home, and you get to work, but ultimately, you're in the same car)

A Three part form like A B C is more like "driving from home, to work, then the supermarket" and ending the story there.

Interestingly, a lot has been said about the philosophical and psychological aspects of "return". Therefore, Ternary form has somehow achieved a "better" status in our minds. This has unfortunately led Binary Form to a "lesser" status, but it hasn't always been so (nor should it be).

In GENERAL, Binary Forms were somewhat more common before the Classical Period, and Ternary Forms became more and more common (to become the more predominant form) from the Classical Period onward. HOWEVER, that doesn't mean you as a composer should favor one over the other - or any other form for that matter.

As in Binary, in CPP Tonal music, what defines the B section is a new key (and of course new melodic material as well). Often, the idea of "Home-Away-Home" is indicated by "T-?-T" = Tonic to some other key, back to Tonic.

But like Binary, there are some common modulation schemes you should know about.

If the work is in Major, the B section will most likely be in the Dominant key, or, possibly in the Relative Minor.

If the work is in minor, the B section will likely be in the Relative Major, or possibly in the minor dominant key (so if cm, B section will be in gm, NOT GM!).

But unlike continuous Binary forms, the first A section does NOT usually modulate to the new key - it instead cadences in the Home Key. B sections will also remain in their new key and cadence in it. What this means is that the A section and the B section are usually "complete" in themselves. Theorists have therefore called Binary Forms "open" (and can still be sectional or continuous) and Ternary forms "closed" (which interestingly kind of parallels the "driving to X" idea above, but not for the same reasons).

The two A sections don't have to be IDENTICAL. What they need to do is be fairly identical, and focus on the home key to be considered A sections (and we call a "varied" version of A "A' " (A prime)).

One interesting thing about Ternary Forms is that composers would repeat sections in what might seem an unusual way. Sure, they did what we would see as "obvious":
||: A :||: B :||: A :||

But they also did something that shows that Ternary and Binary (and other forms as well) had an over-riding formal consideration: Two Reprise. As already discussed in conjunction with Binary Form, Two Reprise means the two halves are repeated. For Binary this is obvious:
||: A :||: B :||

But for Ternary, it's a little less obvious. Basically, A is one "half" and B A together make up the second "half", so the Two Reprise for Ternary looks like this:
||: A :||: B | A :||

In the former "simpler" Ternary, one runs across the "Da Capo" (Da Capo Arias especially) where the A and B sections are written out, and at the end of the B section (which ends in some key other than Home) has the marking "Da Capo" (return to the beginning) and the runs through the A section again, usually to its final cadence (in the Home key of course) to the "fine" (so it may not look like Ternary on paper, but when you play through it it is).

Ternary has taken on some interesting modifications. One of the more interesting ones is found in a lot or Latin American music. In works by composers of Spanish descent like Villa-Lobos, Tarrega, Granados, etc. the B section often is in the PARALLEL key - often these works begin in minor, and the B section will be in Major, like cm - CM - cm.

Another interesting thing that has happened is that composers interspersed transitions between sections to "smooth over" the otherwise closed structure - to make the approach to the new keys happen before the "end of the section" - in this way, Ternary Form can take on the "open" characteristics of Binary Form, and this ultimately leads to other tri-partite forms like Sonata Form and so on.

There are thousands of small dances and character pieces in Ternary (and Binary) form. Minuets are often in Ternary Form, and again obviously the "Da Capo" type pieces. It's really worth looking at some of these "simpler" pieces to get a handle on the differences between the two. The problem with larger works that most people look at is that they simply aren't Binary or Ternary, but are more complex forms (there are nested Binaries and Ternaries, Incipient Binary, Sonata Form, Compound Ternary, etc. etc.) and it's often difficult for aspiring composers to get a handle on those larger forms.

Schumann's Album for the Young, or similar "small scale" works (Baroque Dances, etc.) are excellent resources for exploring Binary and Ternary form, and providing models for incorporating those into your own works.

fine.