When a mixture separates into two distinct parts it curdles, eg, if beaten egg is mixed into a creamed sugar and fat mixture too quickly it will divide into two separate parts. Or if butter is added to a sauce too quickly or the cooking temperature of a sauce is too high, it may split into two parts.
If a sauce curdles place a spoonful of boiling water in a clean pan and gradually whisk in the curdled sauce, or lightly whisk an egg yolk in a clean pan over a gentle heat, removing from the heat and gradually adding the curdled mixture.
Home-made mayonnaise is also prone to curdling, this happens either because the eggs are too cold (never use eggs straight from the fridge - let them come to room temperature before using) or because the oil is added too quickly to the mixture.
To save curdled mayonnaise, put a fresh egg yolk in a clean bowl and add the curdled mixture very slowly, stirring continually, adding any remaining oil to complete the recipe.