Kate Bush was writing songs since the age of thirteen when she was pointed out by David Gilmour at the age of sixteen. She signed a contract with EMI Records soon after. During three years, she pursued her studies and gained maturity in her writing. After seeing an advertisement for Lindsay Kemp's Flowers spectacle, she decided to take mime classes with him. Six months later, she took modern dance classes with Anthony Van Laast. Bush began to recording her debut album, The Kick Inside in 1977. She wrote "Moving" the same year as a tribute to her teacher Kemp. She explained in an interview, "He needed a song written to him. He opened up my eyes to the meanings of movement. He makes you feel so good. If you've got two left feet it's 'you dance like an angel darling.' He fills people up, you're an empty glass and glug, glug, glug, he's filled you with champagne." "Moving" was only released in Japan as a single on 6 February 1978 with "Wuthering Heights" as the B-side in order to promote The Kick Inside.
"Moving" follows a chord progression of Dm–C–B♭–F in the verses and Dm–Am–Dm–Am in the choruses. Written in the key of D minor, the song is set in common time with a "slowly" tempo. Its instrumentation includes drums, bass, guitars and electric piano. "Moving" opens with fifteen seconds of whale song sampled from Songs of the Humpback Whale, an LP including recordings of whale vocalizations made by Dr. Roger S. Payne. In an interview with the magazine Sounds, Bush commented, "Whales say everything about 'moving'. It's huge and beautiful, intelligent, soft inside a tough body. It weighs a ton and yet it's so light it floats. It's the whole thing about human communication—'moving liquid, yet you are just as water'—what the Chinese say about being the cup the water moves in to. The whales are pure movement and pure sound, calling for something, so lonely and sad ..." According to Dr. Ron Moy, author of Kate Bush and Hounds of Love, the lyrics evoke different aspects of Bush's songs : love, relationships, sensuality and desire. She is direct and assertive in the lines "Touch me, hold me/How my open arms ache" while she is more poetic and metaphoric in the line "You crush the lily in my soul."
The Kick Inside was critically acclaimed, AllMusic and Billboard considered Moving as one of the best songs on the album. As "Moving" was only released in Japan, sales and commercial performance were limited. The song failed to chart on Oricon Singles Chart.
Soon after the release of The Kick Inside, Bush performed "Moving" alongside "Them Heavy People" on 25 February 1978 on the BBC's show Saturday Nights at the Mill. On 12 May, she took part in a Dutch special TV show dedicated to the opening of the Haunted Castle, the new attraction of the amusement park Efteling. She performed six songs in six videos filmed near the castle and across the park. At the beginning of the "Moving" video, the camera shows a tombstone covered with leaves. Then, the wind blows the leaves and lets appear the name of Kate Bush. She performs the song in front of the castle's door. In June 1978, Bush sang "Moving" at Nippon Budokan during the Tokyo Music Festival. The performance was retransmitted on the Japanese television on 21 June and was followed by a 35 million audience. She won the silver prize alongside the American R&B band The Emotions. In 1979, Bush included "Moving" on her first tour, The Tour of Life. Her performance is viewable on the video Live at Hammersmith Odeon. However, Bush did not perform the song on her residency show Before the Dawn (2014).