If you go to Pages and edit the page you have selected as the home page there should be a check box just below the edit screen.
You might need to enable it from the “Screen Options” tab which is located at the right top of the edit screen. Click to expand it then check the “Discussion” box – this will enable the check box mentioned above.
Once you have unchecked the box re-save the page and the comments section will be removed (this is assuming there were no actual comments but the comment form) – if however you already have comments on that page then you’ll need to go in to the Comments section and either Trash or unapprove them.
Regards,
Zulf