Spatial complexity is a big word, but in simple terms you could imagine it as the difference between a landed house and a condominium. If only one level is occupied like in the house, you get less room to live compared to if you build upwards and have multiple floors.
Like a multi-storey building, spatial complexity means that space can be used more efficiently by living in higher structures. Higher spatial complexity also means higher resource density for animals using the area. Some animals use only one layer of the forest, while others can move through the layers depending on time of day.
Much of the activity of the forest can happen beyond the reach of humans at the upper levels of the canopy. Combined with dense understory layers, many animals are able to hide from humans, giving them room to carry on with their lives without having to encroach on humans.
How is spatial complexity accomplished? The easiest way is to mimic the natural rain forest and plant in layers, so that all the space from the soil all the way to the tree tops have space for animals to use.
With land being scarce in cities, we have to think about how to use what we have more efficiently. Increasing the amount of vertical space available is one way to do so.