used in modern graphical user interfaces
to represent a single option
which may be selected
Checkboxes are usually square in shape, so as to distinguish them from radio buttons, which are circular. Checkboxes may be found alone or in groups of related options, but in general the state of one checkbox does not affect that of the others. (If one checkbox does control the state of others, they may be drawn indented below the controlling box, in a fashion reminiscent of an outline.)
Almost always, a checkbox represents a binary option -- it can be either on or off, checked or unchecked. The user can select or deselect an option by clicking in the checkbox, or sometimes on its descriptive text. In most GUIs, a selected checkbox is marked with an X or a check mark (a tick mark, to the Brits in the audience), whereas a deselected one is empty.
In rare cases, a checkbox can have an intermediate state between checked and unchecked. For instance, if a group of checkboxes are arranged in outline form -- with some allowing the user to select or deselect large swaths of sub-options with a single click -- then a "partially checked" state may appear. If some, but not all, of the sub-options of a higher-ranked checkbox are selected, the higher-ranked checkbox will appear partially checked. Usually, a hyphen appears in the box.
Checkboxes, like many other interface elements, can be greyed out when the options they represent do not make sense, or are unavailable for other reasons.
The design of the checkbox widget comes from similar boxes found on paper forms.