So you've decided to make homemade mayonnaise and low and behold, it breaks.
Broken mayonnaise means that you've messed up the emulsion process between the liquid (egg yolk, vinegar or mustard) and the fat (the oil).
Don't panic! All you need to do to save your mayonnaise is get a clean bowl, add a teaspoon of water to it, then spoon by spoon add a bit of the broken mayonnaise and whisk. Your mayonnaise will be perfect by the time you're done!