Testosterone increases the rates of muscle protein synthesis post-training, which tends to occur over the long term as testosterone increases the transcription of genes driving increased muscle protein synthesis and, hence, muscle hypertrophy.
Physiological responses are well illustrated in studies where researchers gave subjects supplemental testosterone (which is banned by the World Anti-Doping Agency) and watched its impact on muscle growth. In a famous study from 1996 and published in the New England Journal of Medicine, a group of researchers compared increases in muscle size and strength in a group of subjects given testosterone and undertook strength training compared to those doing strength training alone.
The results were clear; supplemental testosterone had a huge effect on increasing muscle size and strength. The testosterone and exercise group increased muscle size more than 600mm in their quadriceps, compared to a loss of over 100mm for the exercise-only group. They also improved their bench press 1RM by 9kg while the exercise-only group stayed the same.