It was prophesied that Acrisius would be killed by his grandson. In an effort to prevent that prophecy from coming true, he imprisioned his daughter in a tower. Zeus visited her there, however, and she became pregnant.
When he learned that his daughter had a son despite his best efforts, he then places them both in a sealed chest and puts them out to sea. He could not bring himself to murder them but he did not want the prophecy to come true.
The infant is Perseus, who ironically later returns to kill Acrisius for the way his grandfather treated his mother. Thus the prophecy was fulfilled.
