While testosterone is typically seen as a "male" hormone, it's also present (albeit in much smaller amounts) in women. However, between 4-7% of American women produce too much testosterone in their ovaries, which usually leads to a condition called polycystic ovary syndrome.  Too much testosterone in women can lead to infertility due to lack of ovulation, as well as some embarrassing symptoms like acne, a deepening voice and facial hair growth. Reducing testosterone levels in women is often accomplished with medication, although dietary change can make a positive impact also.
The second theory is similar and is known as "evolutionary neuroandrogenic (ENA) theory of male aggression".   Testosterone and other androgens have evolved to masculinize a brain in order to be competitive even to the point of risking harm to the person and others. By doing so, individuals with masculinized brains as a result of pre-natal and adult life testosterone and androgens enhance their resource acquiring abilities in order to survive, attract and copulate with mates as much as possible.  The masculinization of the brain is not just mediated by testosterone levels at the adult stage, but also testosterone exposure in the womb as a fetus. Higher pre-natal testosterone indicated by a low digit ratio as well as adult testosterone levels increased risk of fouls or aggression among male players in a soccer game.  Studies have also found higher pre-natal testosterone or lower digit ratio to be correlated with higher aggression in males.     
As we learn more about how testosterone affects women, the more we will discover how it can either benefit or hinder women in their fitness goals. Testosterone is important to female metabolic, sexual, and muscular function. And just like with men, it is important for women to have a healthy hormone balance. You don’t want too much or too little of any hormone in order to make your fitness goals. Since testosterone is not the primary hormone for women, we will have a lesser concentration than men, but there is a level that is still considered normal for us. As long as we are at this level in the body, we will remain healthy and fit.