Just booked a hoilday and they said they need to check api ??? give passport number what do they check?

why do they need it ? im asking because me and my daughters n=surname has legally changed due to me getting married (to my daughters dad) that's why her name has changed to ?(she now has a new birth certificate will they be able to check this?? my travel agent said we will be ok but never heared of anything like this be for