Checkboxes
Watir sets or clears checkboxes by looking at the attributes available in the <input type="checkbox"> HTML tag. Common attributes are id and name. For complete list see Methods Supported by Element.
What you see in the web browser:
Check Me: 
This is the tag in the HTML source:
Check Me:<input type="checkbox" id="one" name="checkme">
id Attribute
Watir code to set a checkbox using the id attribute:
ie.checkbox(:id, "one").set
Watir code to clear a checkbox using the id attribute:
ie.checkbox(:id, "one").clear
name Attribute
Watir code to set a checkbox using the name attribute:
ie.checkbox(:name, "checkme").set
Watir code to clear a checkbox using the name attribute:
ie.checkbox(:name, "checkme").clear