To nurture something means to supply it with support, nourishment and protection. It doesn't matter what sort of "thing" we're talking about. You can nurture a child, an animal, an idea, a connection with a friend, an attitude, a feeling, a social movement or an organization. If you are inclined to see the universe as a living organism, you can even nurture the universe itself.
The full value of nurturing lies in the fact that it doesn't just benefit whatever is being nurtured. It returns equal benefit to the one who does the nurturing. As Newton observed, "To every action there is an equal and opposite reaction." The act of nurturing also nurtures us in return, in a deep and profound way. Nurturing increases our degree of connection with the world. It helps break down the barriers that separate self from other, that separate each of us from the world we live in. Each nurturing act reminds us of the interdependence of life. If we allow them to, those acts will reinforce our understanding that nothing exists apart from the web of life, and that each of us plays an important role in creating and maintaining that web.
As we nurture, a great sense of responsibility and protectiveness can rise within us. If we use our developing awareness of connection to extend those feelings out to the rest of the world, they will meet and link with our feeling of respect for life. That linkage allows us to create a net of compassion that we can then cast over all life, human and non-human alike.
A great reciprocity rules the universe -- as we nurture, so we are nurtured in return.