Something that's frangible is breakable. You might scold your little sister, "Hey, don't throw that plate like a Frisbee! It's frangible!"
Frangible things can be broken, and they're especially likely to be described this way if they're brittle or crumbly. If your pizza crust is thin, crisp and cracker-like, you can call it frangible. The pages of a very old book you find in your attic might also be frangible. More figuratively, you could describe your easily injured feelings as frangible too. The Latin root is frangere, which means "to break."