Most tree growth occurs at the tips of branches and the tips of roots.
However, while the crown of a tree is usually surrounded by open air, roots need a source of oxygen in the soil in order to grow. In the ground, air and water are held in little pockets called soil pores. If the soil is dense and compacted (with no soil pores), there will not be enough oxygen available for respiration. Too much water in the soil will also limit the amount of oxygen the roots can take in.
Tree roots grow best when they have sufficient growing space and well-drained soil with enough oxygen and water (but not too much water). The depth that oxygen can reach depends on the type of soil and amount of compaction, and the most oxygen will be found near the surface of the soil. For this reason, roots tend to grow right under the surface.