At approximately 2:10, a back-masked voice is heard repeating what has been variously interpreted as a "god with horns" or a "god with hooves" to the sound of a crackling fire and a distant church bell. This becomes even more apparent when the extract is slowed down.
While this has been interpreted by some as a satanic reference, it is notable that this could in fact be a reference to Wicca, a neo-pagan religion descended from ancient Celtic polytheistic beliefs.
"It is commonly understood that most Wiccans worship two deities: the Goddess, often associated with Gaea or Mother Earth, and her consort the God (sometimes known as the Horned God). These two deities are usually thought of as equal complements to each other, and together represent all aspects of the universe" (from wikipedia).
Another possibility is reference to the Greek god of nature, Pan. A satyr, Pan has both hooves and horns, and nature is a recurring theme throughout the music of the Boards of Canada.
A poem called The Pipes of Pan, written by Viavianne Crowley on her book Wicca: The Old Religion In the New Age, alludes to the horned god:
The Pipes of Pan In caverns deep the old Gods sleep But the trees still know the lord And it's the pipes of pan, which call the tune In the twilight in the wood The leaves they dance to the goat god's tune And they whisper his name to the winds And the oak trees dreams of a god with horns And know no other king.
[Snitz] suggests that the source of some samples during the section with the backmasked "a god with horns" voice (the "fire", the "screams", and the chuch bells) is the film "Mirror" by Andrei Tarkovsky. View this video for the samples. The "fire" is in the first of the three scenes, and the "screams" (which they are not in the film, but rather whispers of wind) and the bells can be heard in the second of the three scenes, which starts at 2:20 in the linked video.
Slowed flute from "When the Music Starts to Play" by The Incredible String Band.
4:08 - looped voice saying "take my hand", "to land", or "too late"
On the 2002 website, "take my hand" appears in the scene "seven forty seven". If you fly up to a suitable "pillar" you'll hear it a bit more clearly on its own.
[sandrail] suggests there may be a voice saying "come help me" during the backmasked speech.
Many other works, in music as well as other media, feature the Horned God. Some notable examples are:
Slaine originally came to prominence in the comic 2000AD.
The most notable nods to Wicca are in the eponymous Horned God cycle.
[BIBIO] has made very perceptive observations on this track, and some others:
If you take the section of You Could Feel the Sky where the reversed speech "a god with horns" occurs, and reverse it, then the reversed section of track (normal speed) contains crackling fire sounds, as though some sinister ritual is taking place. However, slow down the reversed section by a factor of 3, and new and disturbing details will become apparent. The sibilant S at end of "horns" is resolved as a woman's screams, and a tolling church bell can be heard in the background. (This has been confirmed - try it yourself if you can). [BIBIO] observes that the acoustics might be those of a forest.
On colours: [BIBIO] notes that the "yellow" in Alpha And Omega seems to repeat continuously at a lower volume; that Music Is Math has a faint voice which could be saying "purple", and that playing the end section at half-speed results in what sounds like "red" being repeated. With the "orange" in Aquarius, they might be trying to cover the range of rainbow colours.
Repeated allusions to flying (in this and other albums): an aeroplane drone in an eagle in your mind; corsair as a type of plane; comments about going to high altitudes for inspiration; Kid For Today possibly containing a looped aeroplane drone throughout the track; an interview picture of BoC in an airfield with planes ("the secret life of Boards of Canada photo). Also the interactive scenes on the BoC website: the introductory scene is of aeroplane contrails, and many of the other interactive scenes are flight simulators. Chinook is a kind of helicopter, among other things.
[SapaInca] thinks that "a God with Horns" rather then refering to the devil could refer to the Wiccan God. He found that whilst searching Wikipedia about Shamanic rituals and such: "It is commonly understood that Wiccans worship two deities, the Goddess and the God sometimes known as the Horned God". There's some more text about that "Horned God" on Wikipedia  and information about Wicca .
[Leo B] pointed out that the second occurrence of the phrase is at 2:16 in the track. 216 = 6×6×6. Given all the other references of this kind (such as the album length of 66'06" (666), it is at least plausible that this is no coincidence). However, see below on whether the time IS 66'06".
From the Spanish language Mondosonoro interview (see the links page), which BoC say that they were really pleased with the beat in this track, which sounds like a taut tope being pulled across the hull of a wooden ship.
[Wikao] notes the sound heard immediately as the track begins may be that of cork being harvested.