In modern parlance parody has come to mean 'a comedic take on an existing song' - singing new words to the same tune which often take potshots at the original creator or theme. But in a wider sense any new work of art built on the musical or poetic structure of an existing work is a parody. So, for example, you could write deadly serious lyrics with the rhyme scheme and structure taken from a poem. Shakespeare's Sonnet 130 (My mistress’ eyes are nothing like the sun) is a parody of traditional love poetry forms. The hymn Love Divine All Loves Excelling (Charles Wesley) is a parody of King Arthur (Fairest Isle, All Isles Excelling) by John Dryden - a poem celebrating sexual freedom. You can also parody musical styles (sometimes referred to as pastiche).
This is a great way to push yourself out of your default patterns.
Back In The USSR
Happiness Is A Warm Gun (Doo Wop style in final section)
I Got A Woman (Ray Charles) – A love song in a stylistic parody of gospel music
The Elements (Tom Lehrer) – The Major-General's Song (Gilbert and Sullivan)
Sowing The Seeds Of Love (Tears For Fears) – stylistic parody of The Beatles!
Weird Al Yankovic is the master of parody. Compare the following tracks to the originals to appreciate his skill in matching phrasing, rhyme schemes etc
A Complicated Song (Complicated - Avril Lavigne)
Jerry Springer (Two Weeks – Barenaked Ladies)
Ode To A Superhero (Piano Man – Billy Joel)
The Saga Begins (American Pie – Don McClean)
White And Nerdy (Ridin Dirty - Chamillionaire)
Word Crimes (Blurred Lines – Robin Thicke)
Serious Like Weird Al (pt.2)
Ticket 19: Different Bar Blues
Ticket 33: Subvert A 12 Bar Blues By Altering The Chord Sequence
Ticket 34: Disguise A 12 Bar Blues Song By Avoiding The AAB Lyric Structure
See the full list of songwriting tips here - Tickets To Write