Intonation is the foundation of the accent (followed by linking and pronunciation). The cartoon is a clever play on word stress.
Wríter's block is the temporary and psychological loss of ability to write.
A writer's blóck is a piece of hard material belonging to a writer.
Other pairs are:
a white house / the White House
a dark room / a dark room
a black bird / a blackbird
a green house / a greenhouse
The first of each pair is just a description, but the second set is acompound noun. The White House is where the President lives, adarkroom is where photographs are developed, a blackbird is a specific kind of bird, and a greenhouse is a glass building for plants that need protection from the weather.