Budgetary slack happens when a person or department that is involved in making a budget manipulates that budget for the sole purpose of making themselves look good. In order to do that, they deliberately overestimate the costs that they will incur or they deliberately underestimate how much product they will be able to turn out. This will make them look good later when they are able to do more than they have predicted and spend less doing it.
You can easily think of examples of this. Let's say, for example, that you are the sales manager for the Northwest Region for a company selling agricultural products. You estimate that you will be able to sell 1,000 tons of fertilizer in the first quarter of 2011. But you know that you are more likely to sell 1,200. When you do better than your estimate, you look good. You have done so by creating budgetary slack -- the difference between what you said you could do and what you really could do. This helps make you look good but it doesn't help your firm.