A native tree is one that evolved within a given local ecosystem and therefore participates fully
in its intricate plant/animal/fungal/soil interactions.
Most invertebrates such as caterpillars can only eat the plants with which they evolved. Most baby birds can only eat invertebrates. When we replace the native plants with non-natives such as turfgrass, Bradford pears, or Autumn Olive, we lose the birds! And we lose the frogs, fireflies, dragonflies, butterflies, etc.
The entire ecosystem (which includes humans) depends on the native plants.