For example, suppose you find out from the 1911 census that your ancestors had more children than have survived to that date, most likely born and dying between previous censuses. If the surname is quite popular for a particular area, you would have to order a lot of certificates to find the missing child. However, if you know the mother's maiden name and it is bit more uncommon, then put just that into the forename field in your favourite search screen for births and baptisms and deaths. Add the father's surname in the relevant field and see what comes up in the time period you believe they may have lived and died within. You may get lucky and find one or more children with the mother's maiden name as their middle name, making them good candidates to be your missing children. This works with Ancestry and FamilySearch - we found missing Arthur Millichip Thomas for one client this way. It doesn't appear to work on FreeBMD though.
You can also use the same technique in reverse to find illegitimate children of a known couple - the father's surname was often given to the child as a middle name by the single mother, sometimes with his blessing, sometimes not! It's worth checking parish registers for the year or so before a couple's eventual wedding to see if there might have been earlier children ... and don't forget to check the burials too in case they did not survive.