Meaning of 'assumptions' specifically in Psychology?

The assumptions of a psychological approach refers to the main ways in which they explain behaviour.
For example, an assumption of the biological approach is that the behaviour is down to three main things; genes, biochemistry and biological structures.

Very good explanation above. So when attempting to explain behaviour from a behaviourist approach, it is assumed that we are all born a blank slate (often referred to as 'tabula rasa' - Latin for blank slate) for our experiences to write on as in we learn behaviour from our experiences, and that only behaviour that can be observed is important.

A behaviourist may also assume that 'nurture' is much more important than 'nature'.