'Biosocial' simply means that a theory deals with both biological and social factors. It's worth knowing two, and we have looked at Money & Ehrhardt's biosocial theory and Eagly & Wood's Social Role Theory.
Money & Ehrhardt developed their theory based on research with abnormal individuals born with 'ambiguous genitalia' - somewhere between a penis and vagina. Their theory is basically that the factors we covered in our look at Social Learning Theory (parents, peers, the media and schools, through reinforcement, modelling and direct tuition) are the key shapers of gender identity, but with labelling as 'male' or 'female' based on biology at birth, and hormones (especially at puberty) interacting with the socialisation.
They supported their claim that a child's gender could be simply reassigned as long as the process was started before they were two with the Bruce/Brenda/David Reimer case study. Of course, the truth of this supports the claim of the biological approach that prenatal hormones are crucial to gender identity.
Eagley & Wood put a 'social constructionist' twist on the claims of Evolutionary psychology. Their theory states that biological differences between the sexes have evolved, but not behavioural differences. They state that these arise through socialisation, but due to the 'social roles' which are assigned to men and women (by society) based on their physical differences. Furthermore, they claim that hormonal differences between men and women are largely due to the different social situations they are encouraged into (men have more testosterone because they are competitive and hostile, rather than the other way round).
Here is a 'colourful'
presentation which has some more details, and here is an exemplar
essay written by a helpful psychology teacher somewhere - careful though, it's not necessarily great!