No, it just reads the information from its data source

You can't edit repeater control but you can design it by
your own

Yes We Can Edit Data In a RepeaterControl,it is based on our
designing 
Example:Display Data What Ever YOU want in Labels and same
data in to Textboxes(visible = false) while page is loading
and  when user clicks Edit Button put all labels to visible
false and and all text boxes to visible true,
foreach(control con in Repeater.Items)
{
  foreach(Control ctl in con.Controls)
  {
    if(ctl is TextBox)
     {
       ((Textbox)ctl).Visible = true;
     }
    if(ctl is Label)
     {
       ((Label)ctl).visible = false;
     }
  }
}

After This Iterate Through All Items in Our Repeater Like
for(int i=0;i<Repeater.Items.Count;i++)
{
   string txt =    
((Textbox)Repeater.Items[i].FindControl("Textboxid")).Text;
}

Get The Edited Text Like This And Update into Database