An expression that states that people may behave or act a certain way as a result of the environment they live in. So for example if someone lives in a poverty stricken area and cannot get a job, they may become a thief. If someone grows up in an environment such as Communist China, that person may become a Communist himself.
“You hear it in the strength of my voice and in my rhythm, Now you know, how I was livin, It happened to me, like it happened to Serch, Prime Minister Pete Nice`ll kick the verse, in Bed-Stuy with my boy, Kiwai Height, The K to A Kingston, Wednesday night, To the Empire, show slammin, Open for Dana, crew flammin, Mouth open wide, or listening, Dumb dope with a forty in my system, Unprotected but respected for my own self, Cause of talent, no shade, or nothin else, A time of tension, racially fenced in, I came off (and all the brothers blessed him), I left more than a mark, I left a dent, Cause I'm a product of the environment.” – Pete Nice of 3rd Bass (Hip Hop Group)
It means that the person you are is a direct result of how you grew up. The "environment" you were brought up in influenced the decisions you make now. Your environment makes you who you are.
So for example, product of the environment implies that if one grows up in a home full of domestic violence, one of the children in that home may become violent as well when they have a family of their own. If someone grows up in the hood, that person may become a gangster. If somebody grows up in a descent home that is filled with good resources (computer, good books, television, radio, etc.), then they are more likely to become successful. If somebody grows up in a Christian home, they will most likely become a Christian. If somebody grows up in the Middle East or in a home with Muslim parents, they are more likely to be Muslim.
A caged animal becomes a product of his environment; mankind however builds his environments to suit his needs. If someone claims that you are a product of your environment, it means the environment you live in, has become your accepted norm, and now it influences you, rather than you influencing it.
Being a product of the environment is no different than saying you are the product of your own thinking.