The song is divided into two parts, which are the first and last tracks of the album. Both are in stark contrast to the album's middle three misanthropic songs, and suggest that companionship can help us overcome our flaws. Waters apparently refers to himself as a "dog" in Part 2: "Now that I've found somewhere safe to bury my bone/And any fool knows, a dog needs a home/A shelter, from pigs on the wing." Another allusion is found in the line "So I don't feel alone, or the weight of the stone", which refers back to the dogs being "dragged down by the stone". Without the track on Animals, Waters thought the album "would have just been a kind of scream of rage".
According to Nick Mason, and confirmed by Waters, it is a love song directed towards Waters' new wife at the time, Carolyne. She was really the only one of Waters' friends he had ever met who could hold her own in an argument with Waters; according to Mason you had to be very good with semantics to win an argument against Waters. Waters wrote the song because that's all he had been looking for all along: someone who could stand up to him, an equal. The former piece of the song conveys a theme of despondency and isolation imposed upon the individual resulting from the societal pressures which work to separate the masses, a theme developed in the following track, "Dogs". Waters conveys a hopeful theme in the latter portion of the song, illustrating the strength and emotional safety as a result of unity among individuals, a safety Waters felt quickly upon meeting Carolyne.
The songs are constructed simply and feature no instrumentation besides a strummed acoustic guitar played by Waters.
A special version of the song was made for the 8-track cartridge release. The 8-track format featured a loop-play function where the end of the cassette was looped with the beginning of the cassette, allowing an album to play continuously without having to turn over the cassette. To exploit this feature, the special 8-track version of the song linked part 2 and part 1 with a guitar solo, performed by Snowy White. Snowy would later play the guitar solo in live performances on the 1977 In the Flesh Tour. The complete version of the song, including the instrumental bridge, was re-released on Snowy White's Goldtop compilation album in 1995.
In a review for Animals, Brice Ezell of Consequence of Sound described "Pigs on the Wing (Part One)" as "a brief acoustic framing device. Its major key signature is a clear contrast to the frequently sinister riffs that form the landscape of "Dogs", "Pigs (Three Different Ones)", and "Sheep"." Ezell would describe "Part Two" as "a reminder that humans find ways to stick together even amidst the turmoil of a cravenly capitalist world."