In the Great & Small game, "spandrel" refers to secondary traits that animal characters can acquire through adventuring and experience. In most cases, these will be the traits of other species, but in campaigns with classic or modern fantasy elements, they can also be magical "items" that become part of the character's biology.
Any time an animal character overcomes a significant (as defined by the BM) challenge posed by an NPC from another species, the BM can reward her by granting her one of that character's Species Traits as though it were her own, permanently adding it to her repertoire of abilities.
For example, a rabbit PC who defeats a dog that was trying to eat her or her friends could be rewarded with one of the dog's unique traits, such as Ultravision, Versatility, a +2 on lore checks to understand longpaw devices, or perhaps the dog's better base Movement Rate.
The in-game explanation for precisely how this transfer occurs is up to the BM. Spandrels are a kind of "magic" or treasure for animal characters, and shouldn't be any more (or less!) of a hassle to acquire than standard magical items for longpaw characters.
Speaking of standard magical items, their powers, too, can be acquired as spandrels by animal characters who discover or encounter them, assuming the item cannot be used as-is by the animal. For instance, animals can benefit from potions by drinking them, just as longpaw characters can (however, potions are subject to the Dosage & Target Size parameters described in the Herbalism document). In settings like the Trucewood Vale, where sapient animals and humanoids interact on a fairly regular basis, collars can be enchanted with the same sorts of magic as rings, and suits of magical armor can be made for non-humanoid species.
In most cases, however, animal characters will have to gain a magical item or weapon's benefits by eating it, either partially or completely (depending on both the size of the item and the size of the character). Standard magic items aren't entitled to a saving throw to resist being consumed in this way; it is simply how the gods have decreed that animals can access magic from longpaw-crafted items. Artifacts and relics, however, are entitled to saving throws, and are difficult to digest in any case.
Eating a magic item or weapon does not alleviate an animal's hunger, so she will still have to rely on normal sources of food for that purpose. Nor does eating the item harm her in any way. It does, however, transfer its powers to her as though she were carrying it as a normal part of her body (note that this does not increase her mass in any way). Magical weapons transfer their effects to one of the character's natural attack forms, and magical armors improve her natural AC.
For instance, suppose a lion Warrior uncovers a cache of longpaw treasure that includes a sword +1, +3 vs. dragons. If she eats this sword, the magical bonuses will be transferred to one of her natural attack forms of her choice... say, her bite. Henceforth, one of her natural attacks will be bite +1, +3 vs. dragons.
Similarly, a snake Magic-User who recovers and eats a wand of magic missiles will gain the ability to cast that spell at will a number of times equal to the wand's charges.
The remnants of a partially-eaten magic item are no longer magical. Their effects have been completely transferred to the animal who ate them.
Finally, magical spandrels can be claimed by foes who defeat their possessors, just as Species Traits spandrels can be. Thus, an animal who defeated the lion Warrior described above could claim the bite +1, +3 vs. dragons as her own. In these cases, however, the spandrel retains its current form and cannot be converted into a different natural attack; the magical bite attack remains a magical bite attack ever after, no matter which species claims it.
It should be emphasized that, for unknown reasons, longpaws cannot transfer or acquire magical spandrels in this fashion; they must rely on using magic items in their standard forms. Similarly, longpaws cannot claim the Species Traits of other animals for themselves (without special rituals), nor can their Species Traits be claimed as spandrels by animals. The BM is free to concoct any campaign-appropriate explanation for why this is the case, but it is a hard and fast rule of Great & Small. Altering it will significantly impact the feel of an animal fantasy campaign setting.
Spandrels with permanent or continuous effects are hereditary, and pass from one generation to the next, just as family heirlooms do in human families. Thus, a lionness can pass her bite +1, +3 vs. dragons on to one of her children if she chooses. However, she will herself lose the benefit.
Even so, there appear to be exceptions to this rule. It is believed by some scholars that the spandrel process is the origin of chimeric creatures like gryphons, jackalopes, or owlbears, animals who combine the traits of divergent species in a way nature can't do on its own.