None of these are for children. Recommended age: 12 and up.
The Ideas Behind the Chess Openings, Reuben Fine gives a useful introduction to most chess openings with easy to read explanations. This is a good place to start for players who want a general introduction.
Winning Chess Openings, Yassar Seirawan focuses on white and black lines in 1.e4 and 1.d4. For intermediate players.
Modern Chess Openings [MCO-14], Nick DeFirmian. This is the 14th edition of the classic opening encyclopedia. There are explanations of each opening system, but this book gives many variations in long lines with evaluations. Useful for the intermediate player but not for the absolute beginner.
Nunn's Chess Openings, John Nunn. A somewhat more detailed treatment than MCO-14, with coverage of most modern opening lines.
Standard Chess Openings, Eric Schiller is a popular version of the the chess encyclopedia, but is considered less accurate than Nunn's and MCO-14.
The following books are readable, stress concepts rather than memorizing lines, and are suitable for age 13 and up.