The other day, I went to a bookstore and saw that there was a "児童" section, which means children's section. But more often in books, I see "子供" used instead. When to use each of them?
児童 is defined in the School Education Act as children from the age of six to twelve who goes to elementary school and in some laws like the Child Welfare Act as children under eighteen.
児童 is used in formal names like 児童養護施設 (children's institution), 児童相談所 (child consultation center), etc. That is to say, 児童 is a formal and legal word for children whose age is under eighteen.
子供 generally means a child as indicated in the following link, こども【子供】
子供 is a common word eqivalent to child (children) and kid. 児童 is a big word for 子供, which is used in formal and legal usages as in "児童文学," "児童教育,"and "児童相談所" as Yuuichi cited.
I thought we can say ”幼稚園(保育園)児童. But 新明解国語辞典 published by Sanseido defines "児童" as "(小学校に在籍する)子供 - child (or children) (who goes to elementary school) with "who goes to elementary school" in parenthes.
When to use each of them?
The other answers saying that 児童 is a more formal word for 子供 are correct, but they don't point out by far the most obvious distinction between these two words. Nobody calls their own children "私の児童" or someone else's children 田仲さんの児童, yet you can refer to even your adult children as your "kodomo". So 児童 strictly refers to children as an age-related thing not as a family relationship.