The word "nature" can be defined in several different ways. The one which makes the most sense here, and yields to most interesting answers, is the Wordsworth idea of a natural physical environment consisting of trees, mountains, lakes and rivers. This is opposed to the built environment of a city or town, or even highly formal gardens, in which nature has clearly been tamed by man.
Wordsworth believed that being in a natural environment could make you a wiser and better person. In "The Tables Turned" he urges the reader to "Let Nature be your Teacher," and continues:
She has a world of ready wealth, our minds and hearts to bless— Spontaneous wisdom breathed by health, Truth breathed by cheerfulness. One impulse from a vernal wood May teach you more of man, of moral evil and of good, than all the sages can.
The moral and spiritual benefits of being in nature which Wordsworth remarks stand alongside gains to physical and mental health noted by various scientific studies, such as the one conducted in the United Kingdom by the university of Derby and the Wildlife Trusts in the attached BBC article. Spending time in a natural environment has been shown to reduce depression and anxiety, as well as such illnesses as hypertension, and to improve overall mood. Beyond these points, we are all reliant on nature in a more direct and elementary way, since we depend on natural processes for the food we eat and the air we breathe. If plants ceased to photosynthesize, or bees stopped pollinating flowers, humankind would not survive for long.
