From Halopedia, the Halo wiki
A battle is a specific instance of combat in warfare between two or more parties or army's wherein each group will seek to defeat the others in various forms of combat, whether on a planet or in space. Battles are most often fought during wars, or military campaigns within wars, and can usually be well defined in time, space and action.
An operation is a planned military offensive, generally against a specific enemy objective or group of objectives. Operations can be large scale battles or small, covert insertions. Operations receive unique code words to distinguish themselves from other actions without giving away sensitive information should discussion of them be intercepted by enemy forces.
A skirmish is a brief battle between small groups, usually part of a longer or larger battle or war. Examples of note include the naval skirmishes at Capella and Theta Ursae Majoris during the Insurrection.