Someone is a product of something. . He was product of the first world war. That the first world war had a profound effect in shaping who he is and what he does, how he acts. . He is a product of his harsh environment. Do not judge him to harshly. He is a street businessman, a product of his upbringing on the streets. . I am a self-made man, that takes the blame off nature. Same sort of concept.

It's usually written as "he was A product of the first world war" The phrase isn't used very often. It means that the person was heavily influenced by the particular time period in which they lived, and the fashion, customs, etc. during that time period. Eg: "She was a product of the American Jazz Age. She spent money recklessly, had her hair cut in a bob and went to parties every night." When we say "He was a product of his time" we are usually using the phrase as an excuse for something bad that the person said or did. We are saying that we can't judge the person for doing/saying something because everyone else at that time was saying/doing the exact same thing. Therefore the person was raised to believe that saying/doing that thing was okay. Eg: "Yes, George Washington owned slaves. But he was a product of his time. He was not a racist." You may or may not agree with his kind of excuse. It is often used in historical debates. Hope this answers your question! :)

The other answers are good. You could also use this with regards to education and training. She has some knowledge of English because she is a product of the public schools where English is mandatory. Messi and Xavi are products of Barcelona's youth academy.