Animals are important in the ecology of seeds in a couple of important ways. First, they bring seeds from the parent tree to new a location. They can either transport it already in the digestive tract (as with berries, see below) or to be cached for later usage (as with nuts and other "non-perishables"). Transporting the seed is good in that the offspring is less likely to compete with the parent tree but bad in that the new location may not be a favorable one for the seed. But there's a way of betting on getting dropped off in a place that suits your niche.
Second, some species need their seeds to pass through the gut of an animal before it can germinate. This process, called SCARIFICATION, dramatically increases FRUGIVORE (fancy name for an animal that eats fruit) it digests the fleshy part of the pericarp and begins breaking down the TESTA, or seed coat. Seed coats keep a seed in dormancy by preventing the embryo for accessing the essentials for germination: water, oxygen, and light (temperature too, but seed coat doesn't do much to buffer the embryo from this). The seed coat can be broken down by UV light (as in radishes) or frost/thaw cycles (as in sugar maples) or abrasion or acidification (or some combo of these). Once the embryo gains access to water, oxygen, and light it begins the rapid process of growth. Once the animal expels the waste, include the largely undigested seeds, they're deposited in a nice bed of fertilizer.
For nuts or other species that don't have a sweet, tasty fruit surrounding the seed, an animal that ingests the seed kills its chances of making it to the next generation. What to do? These species are similar to K-selected species, species that put a lot of parental investment into offspring. Nut bearing trees put a lot of energy into supporting the early growth of their young seedlings (1800 calories in a pound of acorns). Most of that energy is stored in carbs, but with ample protein and about a third fat by weight. And that's not for the squirrels. Trees that produce fruits on the other hand put most of their energy into producing large sweet, watery enticements surrounding inedible (and often toxic) seeds. Almost no fat or protein in fruit. So an energy dense nut needs protection. Some have hard shells (walnuts), other produce high concentrations of tannins (acorns). But a squirrel is a tenacious beast. And so an added measure of insurance to guarantee some make it to the next generation is through masting. Mast trees produce copious quantities of nuts in one year followed by 1 or more seasons of want. This pattern avoids a squirrel (or other seed predator) population from syncing up with seed production and just destroying the harvest each year.
Birds are tiny and don't have teeth, and so the fruits aimed at birds are also tiny and don't require much chewing. They also can be high up on a tree and out on tiny branches where a bird can perch. These fruits are often sweet and abundant in each year. Like nectar in flowers, the sweetness is an offering to the disperser: you take my seeds elsewhere and I'll give you this sugary snack in return. And that sweetness takes sunlight to produce. So these fruity fruits (apples, cherries, buckthorn fruits, grapes, etc.) tend to grow in full sunlight. They need to make sure they get deposited in full sunlight and have 2 methods of this. One is by relying on birds, which often perch on edges or fence rows while they digest and then poop out the seeds. The other is by having seeds that are viable for a longer period of time. This way if they're deposited in the forest they can patiently build up a seed bank and wait until an opening in the canopy arises and then spring quickly into action.
Mammals are pretty good dispersers, but don't go quite as far
It's likely that most of our really large seeded or large fruit-bearing trees (e.g. Kentucky coffee tree, Osage orange) had co-evolved with the now extinct Pleistocene megafauna, like giant ground sloths, giant beavers, and mastodons. Their ridiculously large seeds are too large to pass through the guts of most our mammals