While other answers on here give good "key" reasons why one would want to see Revenge of the Sith before The Force Awakens, it is also significant to ANY Skywalker Saga entry (Episodes 4-9) thereafter, because it features the transformation of Anakin Skywalker into the Sith Lord, Darth Vader.
Anakin's Skywalker's transformation into Darth Vader is significant to both the Original Trilogy and the Sequel Trilogy overall, as the entire Skywalker Saga narrative is ultimately about the Sith Lord Darth Sidious/The Emperor being able to destroy the Republic, The Jedi Order, and abuse (and create powerful abusers) out three generations of Skywalkers in order to maintain power over the entire galaxy, while also seeking eternal life...
When one looks at the Original Trilogy, the story is about Darth Vader's children and if, especially his son, will be turned to the dark side, or stay on the light and help his sister free the galaxy! The story ends with the death of Darth Vader, *almost defeating the Emperor, but with Luke returning Vader to light to be Anakin Skywalker once more, upon death, which is in turn significant to Star Wars over all "Force" mythology.
In terms of the Sequel Trilogy, it's two new young leads, one Anakin's grandson (Kylo Ren), the other a mysterious scavenger (Rey), have all of the characteristics of Anakin Skywalker and Darth Vader combined between them, making the audience wonder who "Rey" is and if she will fall to the dark side and/or if Kyo Ren can ever be redeemed and return to the light and become Ben Solo once more?
The story is that of a new generation on path of self discovery by facing the past. Anakin then serves as a figurative ghost that looms over the story/fate of the two leads, while it is later revealed that once again The Emperor has behind many things and is seeking these two strong force users (who also happen to be a DYAD = One soul split between two beings) to fully come back to life and continue his reign. It ultimately is story about breaking this cycle!
To not have seen Revenge of the Sith takes something away from the deeper context that Anakin's tragedy is echoing/rhyming through this ongoing saga and/or it also takes away the darkest of determinations of Darth Sidious' will, since he is the catalyst for the entire Skywalker Saga.