New growth, taken from the base of the tree next spring , allowed to become semi-hard, has potential to root . The basic rule is the more tender the cutting, the easier to root, but also more likely to desiccate. Desiccated cuttings quickly lose the ability to root. So it's a bit of a balancing act between too hardened and lowered rooting ability, and too tender and susceptible to desiccation. Timing is extremely important when rooting cuttings. Senescence of the parent plant is also very important, which can be partially overcome by taking cuttings from recent growth close to the bottom of the plant.
These rules are less important with easy to root species and critical on hard to root species.