A soffit is actually the underside of any part of a building. It could be the underside of an arch, an entablature, or even a flight of stairs. However in terms of roofing a soffit is the underside of a building's eaves, bridging the gap between the roofline and siding.
The soffit is attached to the rafters that hang over the exterior walls that form the eaves. They often house vents that help regulate attic temperatures, and are designed to work in conjunction with vents at the roofs ridgeline to improve the attics overall ventilation efficiency. In newer construction you will usually find soffit vents at regular intervals, however older homes may not have enough soffit vents if any at all. If you are unsure about your home's ventilation check for soffit vents under the eaves. If there aren't any or they appear to be scarce, consult with a building professional to see what you can do to ensure you have proper attic ventilation.