Often when used in reference to families, this may mean discussion of families that includes familial structure that is different from that typical of the dominant culture here in the U.S.; in other words, families that differ from traditional heteronormative, American families.
In this way certain "diverse families" may be those that have parents who are LBGTQ , or disabled, or multi-ethnic, multi-racial, and / or multi-cultural families. This could mean blended families, where one or both partners may be bringing in children from a prior relationship. Or it could be single