Note: Hi, person reading this. If you liked what you read above, well, we have a growing alphabetical list of animal phrases that you may want to give a look. Indeed, there are numerous sayings that mention all kinds of animals: dogs, cats, fish, birds... elephants, and so on. That page will continue to be updated as more animal idioms are added to the site, so perhaps check back another time if you don't see one that you're looking for in particular.
KnowYourPhrase.com - Meanings and Origins of Phrases
Common Phrase Origins and Meanings  |  E-Letter Idioms
Ignoring an obvious problem; Failing to address an issue that stands out in a major way.
* Darill's coworkers knew that he was responsbile for clogging the toilet, so Darill decided to speak up and address the elephant in the room, and then promptly went to unclog the toilet.

* There was an elephant in the dining room this evening when my friend sat down at the table with a black eye, but did not say anything about what had happened to him.
Elephants are the largest land animals on earth. They can grow up to 14 feet (4 m) tall 
and weigh up to 15,000 lb (7,000 kg). A large elephant in a room is not something that's 
easily ignored; it sticks out like a sore thumb. This is comparable to how if there is a big 
issue that people are aware of but none of them are willing to acknowledge it for whatever reason, then it is like there's a big elephant in the room that everyone is intentionally ignoring.

The exact origin of this phrase is unclear, however, the phrase looks to be a relatively recent one, as it is only found in print as early as the mid 20th century, though it's always possible that the idiom is older. According to Wikipedia, the Oxford English Dictionary credits the New York Times newspaper from June 20th, 1959, as the first recorded use of this phrase as a simile. While I would like to find a copy of the newspaper to see it for myself, I am unable to find one, however there is apparently a line from it that reads:

    "Financing schools has become a problem about equal to having an elephant in the living room. 
     It's so big you just can't ignore it."
 E-Letter Sayings
Phrases and Idioms
The meaning of the phrase Elephant in the Room.
Origins for the idiom Elephant in the Room.
Example Sentences