The parentage is told as an embarrassment. A builder offers to wall Asgard within a season and asks for the sun, the moon and Freyja as payment, and the gods accept because they think it cannot be done. His stallion Svadilfari hauls stone so fast that they are about to lose the wager, so Loki takes the form of a mare, leads the stallion away, and returns later having given birth to a grey foal with eight legs. The story does two jobs at once: it explains the horse and it demonstrates the price of a bad bargain.
The eight legs are older than the story. Picture stones on Gotland, several centuries before the Icelandic prose, show a rider on an eight-legged horse being received with a drinking horn, which is generally read as the arrival of a dead warrior. That suggests the horse is first a conveyance between the living and the dead, and that Odin's ownership follows from the function rather than the other way round.
A frequent comparison connects the eight legs to the drum-horse imagery of Siberian and Central Asian practice, where a mount carries the practitioner between worlds. The comparison is old in the scholarship and is worth stating as one, since the Norse material does not describe anything like that practice and the resemblance is being supplied from outside.