Exemptions for Dependents?

Can someone please explain to me Exemptions for Dependents? My husband and I have guardianship/full custody of his brother and sister who are both minors; we have had them since January 2006, so basically for 2 years. We were told that we were entitled to claim them on out taxes last year but just today we received a letter from the IRS asking us to prove that they qualify as our dependants. They told me to look up Publication 105 on irs.gov for Exemptions for Dependents but I am not understanding or having luck finding exactly what qualifies a child as a dependant… when we filed our taxes we also sent a copy of our notarized and Judge signed guardianship/custody papers but they are still asking us this because the children’s father also tried claiming them on his return although we were told that we were supposed to… anyways, can anyone clarify this to me or give me another site to look for that may explain this better to me?