Here's why they are relevant:
* They are only visible to those who have witnessed death. This ties into Harry's emotional state after his encounter with Voldemort and the subsequent loss of his godfather, Sirius Black.
* They are used to transport Harry and his friends to the Ministry of Magic. This adds a dramatic element to the climax of the book and film.
While other flying creatures like hippogriffs, phoenixes, and dragons exist in the Harry Potter universe, the Thestrals are the main flying creatures featured prominently in the fifth book.