Definition: The literary device of rhyming not just the final word or syllable of a line of poetry (in any rhyme scheme; that's not really the issue here), but internal words and syllables as well, preferably in a natural way that fits the poem's meter.
Example: (internal rhyme underlined, different rhyming sound make the couplet):
We seek, though blind, the undefined, our goal
At last to find the unknown makes us whole.
---me, "Response to Koan in Sonnet Form"
(Yeah, so I quoted myself. This is much harder than it looks, so I'm really proud I succesfully pulled off even a little.)
For many more really well-done examples, see "The Raven" by Edgar Allen Poe.
I created this writeup when, in testing the hardlinks to the now-defunct "Inconvenienced", I discovered that there were no writeups on the topic of the literary device in question, and the closest I could find was Inside Rhyme, a nodeshell linked to Eminem and the Inside Rhyme device. The latter is an excellent writeup, but response writeup be danged, my inner lit nerd compels me to point out that Mr. Mathers is by no means the first artist to employ repeated internal rhymes. Likewise, I have a hard time believing there was anything inadvertent about Bob Dylan's use of this device, because I believe in authorial intent. Perhaps Eminem is the first rap artist to really exploit internal rhyme; his lyrics are hailed for their stylistic cleverness as often as they are denounced for the hatefulness contained therein, but I digress...
(28 February 2002) Ouroboros asked if it counts as internal rhyme when a sound inside a line of poetry is rhymed with the sound that ends the line. My instincts say yes, but I'm honestly not sure.