Water and wood do not mix. Hardwood floors are an organic product and their cellular structure responds immediately to the introduction of water. Swelling and decay eventually follow. The problem is not so much with the surface of the floor since this should be sealed, as with the unsealed raw wood of the sides and bottoms of the floorboards.
At the most, you should only use a very dry damp mop, thoroughly wrung out. Most flooring experts, though, recommend that you never use any kind of water on the hardwood. Instead, clean your hardwood floors daily with a soft-bristled broom and dustpan. Weekly, clean with a vacuum that is designed for hard flooring as well as for carpeting.
If you decide to clean your hardwood with liquids, mist lightly with a cleaner formulated specifically for hardwood floors. Since steam is water, keep in mind that steam cleaning hardwood can be damaging, too. Even Swiffer-type mops and cleaning products, vaunted for being gentle on laminates and hardwood, have a greater reputation than they may deserve. As with any liquid-based cleaning method, you must disperse the Swiffer cleaning liquid in small squirts.