Let's say you create a volume discount that gives 20% off when a quantity of 3 or more is purchased on product A or product B.
Product A has two variants. Color Red and Blue.
Now let's imagine your customer has a cart with 3 items. Product A - Color Red, Product A - Color Blue, and Product B.
If sum up quantities is set to a variant, the discount won't be applied since each variant has just quantity 1 in the cart.
If sum up quantities is set to the product, discount would still not be applied since product A has a quantity of 2 and product B has a quantity of 1.
However, if sum up quantities is set to "across selected items", discount will be applied since combination of all the items in the cart constitutes a quantity of 3.