Since BX doesn't have druids, this one is under clerical spells. I wonder if elves had a separate list whether the designers would have placed it there? At third level, it competes for attention with some pretty heavy hitters in the cleric's go-to repertoire. Spells like Cure Disease, Remove Curse, or even Continual Light. So in the vein of other RSAs, let's take a look at this sucker and see what's what.
Growth of Animal (from Cook):
Duration: 12 turns
So basically it doubles the size, strength, carrying capacity, and damage of a non-intelligent and/or "fantastic" creature. It can however, double the size of a normal creature's giant version: . e.g. Giant Hawks, Weasels, Spiders, etc.
The obvious use of such a spell is to get more out of an allied creature. Your mount, your hound, etc. Changing a dog or tamed wolf into a Game of Thrones-style direwolf would give you an edge in a fight, to be sure.
But that's low-hanging fruit. Let's look a little deeper, shall we?
First of all, the spell has a decent range. This means you don't have to be right next to the creature. Secondly, nothing says the animal has to belong to you. Imagine suddenly doubling the size of a foe's mount. Sure he's got a great big horse now, but he's too high up to hit you. Now imagine combining that same casting with a followup Cause Fear. You could also cause a helluva distraction in the enemy camp but suddenly having some bird or beast swell up in their midst. Maybe that rickety bridge they are galloping across won't take another half ton of horseflesh?
Next, keep in mind that sometimes bigger isn't better. That giant spider chasing you Shelob-style through the tunnels? Zap! Too big to fit now. Sure it's temporary, but two hours is a nice head start. Granted, a fifth level cleric probably isn't running from Crab Spiders too much, but you get idea.
I know it's not a spider, but hedgehogs are just so CUTE!