In the countable sense, a verse is formally a single metricalline in a poetic composition. However, verse has come to represent any division or grouping of words in a poetic composition, with groupings traditionally having been referred to as stanzas.
In the uncountable (mass noun) sense verse refers to "poetry" as contrasted to prose. Where the common unit of verse is based on meter or rhyme, the common unit of prose is purely grammatical, such as a sentence or paragraph.
In the second sense verse is also used pejoratively in contrast to poetry to suggest work that is too pedestrian or too incompetent to be classed as poetry.
Of Man's first disobedience, and the fruit Of that forbidden tree, whose mortal taste Brought death into the World, and all our woe, With loss of Eden, 'till one greater Man .... —John Milton (from Paradise Lost)