You can't grab a pillow from your family room and expect it to adapt to life outside on the patio. Most textiles designed for indoor/outdoor use are made from all-weather materials that repel water or encourage moisture to evaporate quickly by remaining porous.
Fabrics designed for use outdoors are usually fade resistant and UV protected, too. They'll look good and feel soft and comfortable for at least a couple of seasons. When you're evaluating fabrics for outdoor furniture, check cushion seams for heavy duty thread and consistent, even stiches. Choose cushions with vents that encourage air flow and quick drying.
Invest in furniture with cushions that can be unzipped and taken apart for periodic airing, repair or replacement. It's also a good idea to buy outdoor furniture outfitted with cushions you can turn and flip. This will help them retain their shape, dry more quickly and fade evenly. Acrylics, polyester, treated canvas and cotton duck are all comfortable, durable fabrics used in the construction of outdoor furnishings. Look for them in upholstered items, cushions, pillows, curtains, blinds and umbrellas.