Hayloft is the area above the stalls/etc where the animals are kept, like an attic maybe? Hay is [still is? used to be as I understand it] stored there so that it can be more easily distributed to said animals. It has a big outer door for ease of getting bales of hay in and out.
Like the door on the top of this one:
Something like this [without the French doors on the left]:
What is a hayloft? `