A rain porch, also called a Carolina porch, is a form of porch very common on older houses in the American South. The defining feature is significant eaves that keep the porch well protected from rain and sun. These porches are also generally sturdy and massive enough that they appear as a extension of the house, rather than the smaller and less impressive porches common in New England.
My experience with these porches is on older houses in North Carolina, and may not apply equally to all areas. However, in my experience, it is common for traditional porches of this sort to have hardwood flooring, decorative railings (generally painted white), sturdy square columns, and a full roof often including an interior ceiling. They are usually covered by a broken-pitch roof or a second roof structure attached to the exterior wall. This roof is supported by heavy pillars set directly on free-standing supports (usually of brick), although the area between supports may be filled in to resemble a full foundation. They generally extend for the entire length of the front of the house, and often wrap around to include all or part of a second side of the house. It is common to see them screened in, although this was not originally the case with older houses.