A mildew smell in a cushion means there is mildew, or mold, growing in or on the cushion. You can identify the mold by its white, blue, or green appearance, aside from the smell.
Mold flourishes in a damp, dark environment where there is not a lot of air circulation. Furniture that you've kept in storage is susceptible to mold, as is outdoor furniture exposed to frequent rains.
A mildew smell in a cushion can result in uncontrollable mold growth on that piece of furniture. If left unchecked, the mildew will consume the cellulose fibers of the cushion and make it rot.
Brush the visible mold off the cushions while standing outside so you don't spread the spores around your house. Leave the cushion in the bright, hot sunlight as for three to five hours, or until it is thoroughly aired. If you can't take it outside, direct a fan on high to the cushion to dry it.
If there is no visible mildew on the cushion but the smell is still present, the mildew is probably in the padding. Take the cushion to a storage company for fumigation.