Priority lets you have some rules apply before others. This is much like Counterpoint with one extra piece of functionality.
In Counterpoint, when setting up Promotional Prices or Contracts, there is a setting called Group Order. That lets you prioritize your Counterpoint rules. In Counterpoint, if you have multiple promotions or contracts set up, Counterpoint will apply the first rule it hits for which the customer or item and that's where Counterpoint stops calculating.
The same is can be true for NRO Catalog and Shopping cart rules. There is one additional feature that NRO has that Counterpoint does not; the ability to continue processing even more rules, after the cart qualifies for the first one.
For example. Let's say you have 10% off specific items, but for a limited time, you want to have 15% off and you don't want for the customer to get 10% + 15%.
The 15% rule needs a higher priority than has the 10% off rule, so that the 15% rule is the first that is "hit," when the cart qualifies for the promotion. On that 15% rule, you'd want "Stop Further Rules Processing" to be set to Yes.
You'd also want to be sure that no other rules were after the 15% rule that you
DID
want to process. To further illustrate this example, let's say you have a free shipping promo and you want that to apply to the cart along with the 15% off promotion.
To summarize, for this example, we have three active promos; 10% off, 15% off, free shipping.
For the cart to be considered for the free shipping promo, we'd set the priority to 1, 15% off to be a priority of 2 and 10% off to be a priority of 3.
That way, both the free shipping and the 15% off would apply to the cart, but because of 15% off's "Stop Further Rules Processing" is set to yes, nothing afterwards would apply to the cart.