Example sentences
ér儿zi子fàng放xué学le了。
My son is out of school.
tā他de的ér儿zi子duō多dà大le了？
How old is his son?
About this word
儿 is "child" and 子 is "child", so the word stacks two old words for offspring into "son". Listen to the tone: the 子 in 儿子 keeps its full third tone, zǐ, because it still carries the meaning "child". That is the reverse of the 子 in 杯子 or 桌子, where it is a neutral-tone suffix with no meaning at all. 儿 also works as a suffix elsewhere, in 这儿 here, 那儿 there, 一点儿 a little, and in those it is toneless and does not mean child. 女儿 is the matching word for daughter, 女 "female" plus the same 儿.
The story behind the character
儿
The traditional 兒 is a baby's head with the fontanelle still open (that gap on top) and two legs below. Xu Shen wrote 儿, 孺子也. 孺子 is a little child.
子
子 is a newborn drawn from life. Big head, arms stretched out, legs swaddled together. The oldest forms are exactly that, and Xu Shen simply marked it 象形, a picture. It is also the first of the twelve earthly branches, the one paired with the rat, which is why the character shows up on old calendars and in the zodiac.