Consonance is a literary device used to create rhyming effect and musicality in a text, especially of poems. It, essentially, is the likeness in rhyming sounds caused by the repetition of consonant sounds of words in a line that are placed in quick succession or close to each other in a line. It is also used to create half rhymes.
That thou consum'st thy self in single life?
(Sonnet 9 by William Shakespeare) line 2
This line from Shakespeare's Sonnet 9 uses consonance as rhyme and half rhyme, with the 'th', 's' and 'f' sounds.
And as the Sonnet progresses the poet uses more consonance, repeating sounds 'th', 'w', 'd' and 'l'
The world will wail thee like a makeless wife;
The world will be thy widow and still weep
(Sonnet 9 by William Shakespeare) lines 4-5
The purpose of consonance is to create musicality and make it easy for listeners or readers to remember the lines. It plays the part of a hook to interest and keep the reader engrossed.