The word "nature" has different meanings. It can refer to the total biological scope of the planet Earth. It can also include the total ecological system of the material world. "Mother Nature" is a term used to describe the whole of the ecological system on the planet Earth.
In philosophy, it can refer to the essence of something. Likewise, theologically, the nature of something is that which makes something what it is. It is the most basic essence of something. We would say that the nature of God is good, holy, just, immutable, etc. If we were to take any one of these properties away from God in describing his nature, he would cease to be what he is. The nature of something deals with the essential properties that make something what it is.
In theology, and in particular as it relates to Christ and the incarnation, Jesus has two natures. That is, he has a divine essence and also a human essence in the one person. The essence of something is revealed by the characteristics it produces. Therefore, the nature of divinity manifests itself in purity, holiness, omniscience, eternal preexistence, etc. The nature of humanity manifests itself in being born, eating, growing, etc.