Assuming that you're referring to the general validity of a (UK) child's passport, this applies:
"If your child is under 16 they need a child passport to travel abroad. They can use this passport until it expires. For example, a 15-year-old who needs a passport must apply for a five-year child passport. They can use this passport until it runs out, in this case when the 'child' is 20.
When a child reaches 16, the next passport they apply for once their current passport runs out should be a ten-year adult passport renewal"
Source:
http://www.direct.gov...ildpassport/DG_174105
If you're referring to the amount of unexpired time which is needed on the passport to travel abroad, the answer varies by country. For travel to ANY country within the European Union, a UK passport only has to be valid on the actual dates of travel. The same applies to many other countries which are popular with British tourists but some countries do require certain minimum periods of validity (which applies to both adult and child passports). To check upon the requirements of any particular country, click on the name of the country here
http://www.fco.gov.uk...el-advice-by-country/
and then on 'Entry requirements'.
Chris