Cupping is an industry term that describes the way a wood floor will sometimes bend, with the edges of affected board becoming higher than the center, forming a concave surface. Hardwood floors do this because they have absorbed excess moisture, with the underside absorbing more than the top. This creates an imbalance of expansion, causing the edges of the top side to curl up and away from the subfloor.
Moisture is the sole cause of cupping, but that moisture can come from any of a number of sources, from high humidity in the air to out and out flooding. Hardwood floors in the basement are particularly susceptible to moisture, and cupping isn't uncommon on decks or patios, which are often exposed to more moisture than indoor floors. Wood floors that are above a crawlspace may also cup because of moisture building up in the space. Leaks from plumbing, doors or roofs may also be a cause.
The removal of water is the first concern. The underlying problems, such as leaks or excess humidity in a crawlspace, must be alleviated and any standing water soaked up, but that alone won't do the job. You want to get rid of as much moisture as you can from inside the hardwood. Dehumidifiers can help, as can fans; even hairdryers, if used on a low setting on a small area of damage, can help. Getting the heat and air to the underside of the floor is best, but not all floors have a crawlspace beneath them. If you have forced air heating, you can dry out damage by turning off any humidifiers, turning the heat up between 75 and 80 degrees F and leaving the furnace blower set to manual so that it will continue running.
Cupping will flatten out over time as the water evaporates and the boards stop expanding. Many will contract back into their original shape but, if the cupping is still clear after the water is removed, you may try a cosmetic solution. As long as there is no buckling (separation between the floor boards and the subfloor), you can sand the floor lightly and across the grain. The boards shouldn't be sanded down to bare wood but just enough to remove the finish and assist in the evaporation of moisture. At this stage, you may want to hire a professional because it's easy to sand too deeply. After the sanding, dry the wood out again using fans and dehumidifiers. If cracks have formed or boards have loosened, you'll need to screw down the boards and fill in the cracks. If the floor has both cupped and buckled, the damage is probably too extensive to fix, and you may have to replace the damaged area and the boards immediately surrounding it.