Here are more formal definitions of poetic couplets, including some of what may vary with their use:
A pair of successive lines forming a distinct thought
Two lines forming a minor grammatical construction, united by rhyme or cadence, and printed and referred to individually
Any of various verse forms consisting of a repeated couplet of long and short or stressed and unstressed lines forming stanzas
A pair of musical strains with similar rhythm
Here are a few famous examples of rhyming couplets from various ages of English heroic verse and other works:
William Shakespeare, Romeo and Juliet:
But, soft! what light through yonder window breaks?
It is the east, and Juliet is the sun.
Alexander Pope, An Essay on Man, Epistle I:
Hope springs eternal in the human breast;
Man never is, but always to be, blest.
William Butler Yeats, Easter, 1916:
I have met them at close of day
Coming with vivid faces
From counter or desk among grey
Eighteenth-century houses.
William Carlos Williams, Paterson:
By the road to the contagious hospital
under the surge of the blue
mottled clouds driven from the
northeast—a cold wind.