Darwin has two first degree relatives named Erasmus. Darwin's older brother was named Erasmus (nickname = Ras) [he also had 4 sisters]. Both Darwin and Erasmus attended the Univ. of Edinburgh to study medicine, and both quit before finishing. This was a disappointment to their father Robert Darwin, who had one of the largest medical practices outside London (in Shrewsbury) at the time. Darwin and his brother maintained close and friendly relationships throughout life and Ras supported Darwin's scientific work.
Your question likely refers to the other Erasmus, Darwin's paternal grandfather, who was a leading intellectual of his day, active in scientific and social matters. Darwin never knew his grandfather Erasmus as he died before Darwin was born, and it was not until later in life that Darwin recognized the genius of his grandfather who was a noted scientist himself. Indeed, in his book "Zoonomia" Erasmus Darwin described aspects of natural science and the liklihood that biological changes (i.e. evolution) occurred over time.