Elegant variation is the attempt to relieve repetition by replacing words with synonyms. For example:
The English lexicographer H. W. Fowler coined "elegant variation" as an ironic criticism of this strategy. Elegant variation distracts the reader, removes clarity, and can introduce inadvertent humour or muddled metaphors. It can confuse readers who are unaware, for example, that the Pope is the Bishop of Rome. It fails to fix the real cause of repetitive prose, which is usually repeated information, not repeated words.
Some newspaper writers were famous for overusing synonyms:
It was around two decades ago [1930s], in the city room of the Boston Evening Transcript, that I first became aware of the elongated-yellow-fruit school of writing. The phrase turned up in a story, a determinedly funny story, about some fugitive monkeys and the efforts of police to recapture them by using bananas as bait. The young rewrite man of the story was bowling along in high spirits, full of references to "the gendarmes" [the police] and the "blue-coated minions of the law" [the police], and it was inevitable that in such a context the word banana would seem woefully dull. So it was that bananas became, after first mention, "the elongated yellow fruit"—a term which the Transcript staff always used thereafter in dealings with the office fruit peddler, especially when the young rewrite man was within earshot. — Charles W. Morton, 1955[1]
Elegant variation is often less absurd than in the examples above – for example, writing "the singer" instead of "Michael Jackson". It's often used to avoid repetition that arises from other problems, such as needlessly complex syntax: a case of treating the symptom and not the cause. Fixing elegant variation isn't always a case of removing flowery language, but making prose clearer and tighter overall. In other words, using plain English.