Focus breathing is a term that refers to a lens changing field-of-view when changing focus. Most typically this means that the field-of-view widens when focusing towards minimum focusing distance.
Most lenses show some level of focus breathing, unless they have explicitly been designed to not ‘breathe’. However with objective-focusing (all lens elements move together) lenses focus breathing tends to be a relatively minor issue, whereas with many element focusing (used mainly in fixed lens cameras), internal focusing and rear focusing lenses focus breathing sometimes is a major factor.