I just discovered, via this excellent article by Jeanette Ostermeyer, that this is a name given to self-created forms — that is, where there is some regularity or pattern of metre, rhyme, syllables, whatever. The specific form is created because it seems to fit the needs of the particular poem. Sometimes, we're told, one of these may take on, be used widely by other poets, and acquire its own name.
The term can also apply to variations on traditional forms, such as rhyming sestinas and unrhymed odes. (I have also come across 10-line sonnets.)
I think maybe we all do a lot of this without even regarding it as anything special. I, for instance, like my stanzas to be the same length even in free verse — whatever length, or variable pattern of lengths, happens to suit the poem. I'm not sure that's sufficient to constitute a new form, however.
One of my widely-published early poems, The Day We Lost the Volkswagen, has a pattern all its own (as far as I know) because it just seemed to need it. It's basically a rhyming ballad (abab quatrains) with an extra line added per verse, and the extra lines rhyme with each other — in a four-verse poem, the last lines of verses 1 and 2 rhyme with each other, and the last lines of 3 and 4 have a different rhyme with each other. (It's a lot more complicated to describe than to read!) I've never used the form again, though. I never felt any need.
(Funny — I once read it to a group of writing students by way of example of something or other, and one who had been listening with an expression of rapt delight, said afterwards, "And not a rhyme in it!"
"Excuse me," I said, "It has a complex scheme of full rhymes."
But I decided to take it as a compliment. I guess that for her the rhymes were unintrusive and the language just seemed natural. That's gotta be good.)
Recently, members of the dVerse online poetic community were invited to create a new form. Because I like to play with a non-traditional or "free" version of the ghazal, and because I also like playing with American sentences, which Allen Ginsberg invented as a Western style of haiku, I combined them both. You're welcome to read the result.
I found that the sentences went neatly into 3-line verses, and the whole had some of the features I like in a ghazal. I called it Ghazal-type 17-3 — which I think a clumsy name, but I hoped it would suggest that there might in future be other, different ghazal-type poems. (Because of my departures from the strict form of the traditional ghazal, I think it's more accurate to say "ghazal-type".)
But I haven't used it again. And I haven't made up any other ghazal-type forms. I make poems in whatever way seems right at that moment, then go on to the next moment.
Ostermeyer, whose article focuses on metrics, alludes to Peter Davison's book, Breathing Room, in which, she says,
"... nearly all the poems conform to twenty-five lines cast in seven tercets and a closing quatrain. These lines are set in a flexible pattern ..."
Perhaps it would be fun to create a form (or even adopt an existing one) and then stick with it for a whole book.