This word is remarkably similar to tsin (the Navajo word for tree or wood).
But you’ll notice the glottal stop (the apostrophe) right there in the middle. Normal ts sounds like the ts in “hats.” So tsin would be like saying “hatsin” without the initial ha. For ts’ the pronunciation will need to be ‘ejected’, so to speak. Try saying “hats” “in” by pronouncing each word separately. Then, repeat those words and bring them closer together after each repetition. You should soon be saying “hats’in” with a distinct explosive ts’. It will feel like your tongue is doing a lot more work to push air out, and you’ll notice your throat (glottis) close up momentarily as you transition from “hats” to “in”. (Once you feel you’ve got it, just take away the ha and you’ve got ts’in.)
So now that you’ve got an idea of how to say it, what does it actually mean?
Whereas tsin means tree, ts’in is actually the Navajo word for bones. You can also say ats’in to mean “a bone”, which is considered non-possessive. Replace the leading a- with shi-, ni- or bi- to create shits’in, nits’in or bits’in, which translate to my bone(s), your bone(s) and its/his/her bone(s), respectively.
For fun, here’s the word for cartilage.