Why and how was the theory of biological determinism used in the past?
Biological Determinism has been used to try to model human behaviour but has also been used to discriminate against races and both sexes for perceived biological weaknesses.
One of the great questions that mankind has sought an answer to is "Why do we do the things that we do? Why do we think and feel the things we do?"
There are two competing theories that have been summarized down to Nature and Nurture . Nature refers to what it is that we have inside of us in terms of DNA and other physical traits that we inherit from our parents and subsequently pass down to our children. Nurture refers to behaviours being learned - that we start as a blank slate and our behaviours and beliefs are driven by what we learn from others.
The Nature side of the argument is the Biological Determinism side - that what we are is a function of biology.
It has been used as a tool to try to understand the body and the brain: the body as a machine, the brain as a computer, etc. It has also been used as an argument to discriminate against various races and both sexes - the thought being that race/sex x has a tendency to be smarter/dumber, better athletes/worse athletes, more prone to commit crime, more emotional, less rational, etc and that these tendencies, being written in the DNA, was an unchangeable fact about a race.
With the discoveries that the brain constantly rewires itself (known as Brain Plasticity) and that experiences can cause the body to recode the DNA through the epigenome (here's an article that does a good job of explaining it), Biological Determinism holds less sway than it formerly did.