A foundation, or a box spring, is designed to support a mattress and keep it from sagging. Box springs allow air to circulate around the bottom of a mattress, helping to prevent moisture build up and reducing the risk of mildew growth. Foundations come in sizes to match beds. Bed frames hold a foundation and mattress, raising them off the floor to a comfortable height. At their simplest, they are bare metal frames, but can be made of wood and may include a headboard or footboard.
A traditional mattress consists of an inner core of metal coils surrounded by padded layers of cotton or wool. To prevent sagging in the center, it requires the support of a foundation. Traditional mattresses are at risk for interior mold growth, so they need the increased air circulation that comes from being on a box spring and from being raised off the floor by a bed frame.
Latex mattresses contain an inner core of vulcanized latex, which is encased in a cotton sheath. At less risk for internal mold growth, latex mattresses don't need the air circulation provided by box springs and bed frames. If you have a platform bed, you may place a latex mattress flat on it without trouble. If you use a bed frame, make sure it has slats to provide even support to the entire length of the mattress.
Bed frames come in standard sizes, so if you replace a queen mattress and foundation with new ones, the same frame works with the new set. Foundations also come in standard sizes, so an old box spring can fit a new mattress. Sales staff may suggest buying a new foundation as well as mattress, but extending the life and comfort of your mattress depends more on regularly rotating and flipping it, rather than having a new box spring.