Children, that is, kept in by Barbara (6)
I believe the answer is:
babies
'children' is the definition.
(baby is a kind of child)
'that is kept in by barbara' is the wordplay.
'that is' becomes 'ie' ('i.e.' can be a synonym of 'that is').
'kept in' is an insertion indicator.
'by barbara' becomes 'babs' (I've seen this before. I am not sure about the 'by' bit.**).
'ie' put into 'babs' is 'BABIES'.
Can you help me to learn more?
(Other definitions for babies that I've seen before include "Small children" , "Recently born children" , "Very young children" , "Infants" , "Storks' freight?" .)