I must confess, I'd never heard of it.
I found this paper:
http://pubs.acs.org/doi/abs/10.1021/ja01219a007If I understand correctly, if you have an acid-base reaction:
A + B
AB
Then F-strain is the strain caused by steric repulsion between A and B. B-strain is is the strain induced within B through geometric changes upon complexation of A.
Brown's example is B = trimethylamine. If you complex it with an acid (A), the C-N-C bond angle is compressed, and the increased repulsive forces between the methyl groups (within B) is the B-strain. The F-strain is steric repulsion between B and A.