When covering ornithischian ossified tendons, I really only just mentioned their existence rather than what they were or what they meant, and the post rather implied that this was a unique situation. Far from it, they turn up quite often as you might have noticed if you ever took apart a turkey and looked at the legs and wings.
Tendons are of course those bits of tissue that connects muscles to bones. However, while this typically requires at least a small degree of elasticity, it is the muscles that really have to deal with that. If therefore you want those tendons to be especially strong and resistant (because they are taking some high loads) then they can be firmed up with a bit of bone. Quite literally part of the tendon ossifies and becomes bony tissue which of course massively increases its strength at the expense of elasticity.
While the ornithischians are of course a good example of this phenomenon, it turns up in other clades too like the nyctosaurian pterosaurs which have lots. Pterosaurs have interesting problems when it comes to attaching muscles on those massive arms and fingers and with the high stresses encountered through flight, it’s more of a surprise that more pterosaurs don’t have lots of ossified tendons than that a few do.
While certain clades or genera are pretty consistent in the way in which tends ossify it can happen in most animals after an injury or a result of unusual stresses on certain muscles groups. This means that the pattern of expression is complex, and while the presence or absence of such tendons can be a useful diagnostic character, they are not necessarily the best ones to adopt. Some specimens of Pteranodon for example preserve ossified tendons, but they are very much in the minority, though of course owing to their overlap in the fossil record and their great similarity, it would be easy to misidentify a couple of wing bones with an ossified tendon as belonging to Nyctosaurus. They also have a role to play in revealing the presence of certain muscle groups since you can’t really get an ossified part of a tendon where there were no tendons to ossify so their presence can be useful when trying to reconstruct the soft anatomy of the animals in question too.