As meat braises, the gentle moist heat breaks down connective tissue inside the meat. This connective tissue (collagen) literally begins to melt, sinking into the meat and making it oh-so-very tender. This takes a long time to happen - up to several hours for larger cuts - and is also why tough cuts with a lot of connective tissue are better for braising.
If you still feel some resistance when you poke into the meat, that means that this connective tissue hasn't completely melted yet. Even if the meat is at the right temperature, it would taste chewy and maybe even a little dry if you took it out at this point. A little extra cooking won't hurt, and you'll be rewarded with super tender and moist meat.
Next time you make a braise, try testing it with a fork or knife every hour during cooking and you'll really see how the texture changes!
What braises have you been making lately?
(Image: Sara Kate Gillingham-Ryan)