Rondo is a type of musical form that is super flexible. Its identifying feature is a recurring melody section that returns multiple times, interspersed with contrasting sections. Sections are usually given a letter to represent them, so some common examples are identified as ABACA, ABACABA, and ABACADA. This can go on for quite a bit, but the 5-part and 7-part Rondo (indicated by the number of letters naming sections) are the most common.[*] Additionally, there might or might not be a transitional chunk of music between sections. Transitions can vary in length, from a couple notes to several bars.
Historically, Rondo dates from the seventeenth century and is not the same as the medieval French form Rondeau, but both have a recurring A section.[†] Rondo is more closely related to Baroque Ritornello form, which was concerto form.[‡]
The differences used to make the contrasting sections vary. Sometimes only the melody is different. Sometimes it’s a modulation to a closely (or distantly) related key. Sometimes it’s a difference in orchestration (how many instruments are play), especially in rondo movements of concertos.
A famous example of Rondo is the Rondo alla Turca by Mozart (third movement of Piano Sonata #11 in A major K331) and the reason I heard the question “what is rondo?” being asked.
Here’s a link to a recording: https://www.youtube.com/watch?v=eTZ33EVK3Ug
This piece is actually a complex Rondo; each section labeled A or B has little forms inside. In this case the second B section is short and the last A melody comes back in not the original key.
Large section: A B A B A
Small section: a b a c d c a b a c a
Key: Am CM Am AM F#m AM Am CM Am AM——
It looks more like a rondo if you’re looking at small sections, but lots of times you can identify a piece’s form only by adding caveats of how it differs from the platonic ideal. There are few pieces that fit exactly into a given box of a formal label.
Here are a couple other examples of Rondo:
Dave Brubeck, “Blue Rondo á la Turk” https://www.youtube.com/watch?v=j9GgmGLPbWU
Anton Dvorak Cello Concerto 3rd mvt: https://www.youtube.com/watch?v=jkflk3aMEis
Jane Vignery, Horn Sonata 3rd Mvt: https://www.youtube.com/watch?v=xfkVdvLSQFA
Germaine Tailleferre, Rondo for Oboe and piano: https://www.youtube.com/watch?v=g1n1wH8JaMo
[*] If you only have 3 sections (ABA), that’s not really long enough to be considered a rondo, depending on who you ask.
[†] For the medieval form: https://en.wikipedia.org/wiki/Rondeau_(forme_fixe)