Many sauces are emulsifications. That is, one substance suspended in another. Vinaigrette, hollandaise, bearnaise, and many more sauces fall into this category. An emulsified sauce involves suspending one ingredient one or more other ingredients. Typically a fat, such as butter, is incorporated into the mixture. The fat can easily separate from the emulsification, breaking the sauce.
Several conditions that will break a sauce:
How, you may ask, does one know if a sauce is broken? If the sauce is overcooked the protein will coagulate, making the sauce appear grainy. The most common break though, happens when the fat is not added properly. One will see pools of fat sitting in the sauce.
Fear not, there are ways to repair a broken sauce. Whisk together one egg and a little water, cook the egg over a double boiler. Then whisk the broken sauce into the egg.