This is a play on words, because nature and nurture sound similar [but not identical]. It refers to the (undecided) debate as to whether we are influenced more by genetics (inherited traits, nature) or by environment (upbringing, nurture).
nature (noun): the physical force (as in Mother Nature) regarded as creating and controlling the physical world including plants, animals, landscape, weather etc
nurture (noun): the process of caring for and encouraging the development of (sby or sthg) - note that "nurture" can also be a verb
In the phrase you quote the implication is that genetics play a greater role than the environment (in a person's development).