Bing Bong was Riley's adorable imaginary friend created during her early childhood. However, as Riley grew older, she stopped playing with him, leaving Bing Bong out of a job and a bit lonely.
Drifting around Long Term Memory unbeknownst to the other mental denizens, he collected happy memories he liked into a bottomless bag. He greatly missed the times he shared with Riley and was desperate to not be forgotten until one day when he is discovered by the misplaced emotions Joy and Sadness, who were accidentally ejected from Headquarters. Afraid of their sudden appearance, Bing Bong initially tried to run, but when Joy presents herself, he is thrilled to meet her. As the two need to return to Headquarters, Bing Bong, who has been forgotten for a long time, agrees to help them, more so when Joy tells him she will put him back in business when she gets back. He proposes that they take the Train of Thought that will lead them directly to Headquarters, and shows them the way.
Unfortunately, since he was created when Riley was a toddler, his naive nature impedes the duo from getting anywhere close to Headquarters. In fact, he leads them into danger in Abstract Thought, which he thinks is a shortcut. Luckily, they escape just in time before they implode. They get out, but soon Bing Bong witnesses the demolition of the childish aspects in Imagination Land with his precious wagon thrown into the Memory Dump in the process, Bing Bong falls into deep depression. Joy tries to get him to stop being sad by making silly faces and doing childish things, but they don't work. When Sadness talks to him, she empathizes with him, and by getting him to express his sadness, she comforts him and inspires Bing Bong to bring them to the Train of Thought.
However, the train stops as Riley is asleep. Bing Bong, Joy and Sadness go to Dream Productions to wake up Riley through a dream by getting Joy and Sadness to dress up as a dog and he starts a party in the classroom with balloons and confetti, and inadvertently creates chaos in it when he starts dancing and caused the dog costume to rip in half and Joy chases Sadness around causing the dream to be a dog chasing the other half. Bing Bong shows himself to try to remind Riley of him, but he is arrested and thrown into the Subconscious. Joy and Sadness enter the Subconscious to rescue him and find him detained inside a balloon prison on top of the sleeping Jangles the Clown, one of Riley's worst fears. Joy frees him without waking the fear up, however, they realize that Jangles is the only way to get Riley awake. The group reluctantly wake up Jangles and run quickly with the mad clown in hot pursuit, leading him back to Dream Productions which causes Riley to wake up in shock.
The three of them finally board the activated Train of Thought. However, it is quickly destroyed by the destruction of Honesty Island. Joy tries to leave Bing Bong and Sadness behind in hopes of making it back to Headquarters in time, but it is too late as the falling debris of Family Island crashes on Joy's location and falls into the Memory Dump, taking Joy and Bing Bong (who was trying to catch Joy from falling) with it. Inside the dump, Bing Bong finds out he is slowly fading and on the verge of disappearing forever and has lost all hope. To get the both of them out of the Memory Dump and save Riley's mind, Bing Bong and Joy try to use Bing Bong's wagon to blast out to the surface. No matter how hard they sing, the wagon falls short every time. Bing Bong, in a moment of self-realization, starts the rocket again and jumps off before it flies away, making the wagon light enough for Joy to reach the top. As Joy looks and realizes what he has done, Bing Bong cheers and tells her to "take Riley to the moon for him", as he waves his last goodbye to her and fades into oblivion. Joy watched Bing Bong vanish as she tearfully promised that she'll try to fulfill his wish.
The film was originally going to feature a whole slew of "imaginary friends", as characters from Riley's early childhood that were now refugees living in a place called "Hobo Camp". In addition to Bing Bong, these included Mrs. Scribbles, who was a stick figure, and "Corner Sun", who was literally a quarter of Sun as kids would draw in the corner of their drawings. Ultimately, this storyline was condensed to just Bing Bong.
After being asked why Bing Bong is made of cotton candy, Pete Docter simply stated, "I like cotton candy."
Bing Bong's illiteracy might come from the fact that Riley created him at a very young age.
Bing Bong's overall fate is very similar to what Woody narrowly avoided in Toy Story 3, both literally and figuratively. Literally in the sense that Bing Bong disintegrates into nothing in a heap after falling in to the Memory Dump, similar to how Woody avoided the incinerator's firey core. Figuratively in the sense that Bing Bong is no longer needed due to the child outgrowing him, similar to Woody's fears through Toy Story 3, and a subconscious fear through most of the Toy Story franchise.
Although he has faded away, it's quite possible that Riley still remembers him, according to The Bing Bong Book. At the end of that book, Bing Bong finds Storybook Land, where three Bing Bongs from books Riley wrote when she was younger appear to join him for tea. This could mean he could reappear.
While saying his last line, "Take her to the moon for me, okay?", Richard Kind was in tears.
As seen in early concept art you can see that Bing Bong was going to have chicken wings and a pig tail at one point.