Chelle7272 is correct in indicating that your children hold British citizenship and can obtain British passports.
However (subject to the laws of the country which you're from), it's likely that your children hold DUAL citizenship, and can also obtain passports from your country of origin.
A few countries don't allow their citizens to hold dual citizenship, but most do. Also most countries recognise the children of one of their citizens as also holding the same citizenship (irrespective of where they're born).
Many people hold two (or more) passports, from different countries. It's perfectly legal to do so. It's likely that your children will each be able to hold two passports, if they choose to do so,
Chris