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Some few thoughts without testing or anything else:

• Cache the value of the cell in a local variable.
• Replace for-loops if possible with foreach-loops.
• The call of boxList[x].Name.ToString() is unnecessary, it is already a String.
• break after setting the visibility to avoid unnecessary checks.

foreach(DataGridViewRow row in dgv.Rows)
{
 String cellValue = row.Cells[1].Value.ToString();
 foreach(CheckBox boxItem in boxList)
 {
 if(cellValue == boxItem.Name)
 {
 row.Visible = false;
 break;
 }
 }
}

On another sidenote, please use meaningful variable names, even in such stupid iterating loops.