The “sons of God” is a little difficult to explain without adding the phrase “daughters of God.” I was raised in the Church of Jesus Christ of Latter-day Saints, and I always heard the phrases “sons of God” and “daughters of God” when I was a child; I still do. Anyway, the reason I have to add “daughters of God” to the original phrase asked about is because they mean the same thing, but they simply reference the two different genders.
When someone says someone is a son of God, they are simply stating their belief that all of us are spirit children of God, and therefore are all brothers and sisters in spirit. This is a core belief for the Church of Jesus Christ of Latter-day Saints.