Something that's old-fashioned is out of style or from the past. You could call an antique telephone old-fashioned, and you could also describe your elderly grandfather this way.
Out-of-date clothes, like your aunt's wardrobe of 1980's dresses with shoulder pads, are old-fashioned. Soda fountains, carriages pulled by horses, and typewriters are all old-fashioned as well. These things are either not currently popular, or they're just plain old. There is also a whisky-based mixed drink called an old-fashioned which is still served in many stylish bars and restaurants.