Complex sentence: Chittrangada died unmarried and Vichitravirya died without issue, and hence their mother asked Vyasa to father the child through the "niyoga" method: fathering the child through transmission of energy to the female without physical touch.
Split into simpler sentences: Chittrangada died unmarried and Vichitravirya died without issue and hence their mother asked Vyasa to father the child through "niyoga" method. Niyoga method is fathering the child through transmission of energy to the female without physical touch.