There are a large variety of two handed swords from a great number of places and eras, many of which had different uses. In Germany, for example, select soldiers carried zweilhander's into battle (16th century). These could be used in personal combat, but were generally more effective as an anti-pike weapon. Katanas can be wielded with one or two hands, and are effective against people in light armor (Japanese armor has historically been made of leather, wood, paper, and laminates rather than metal). Similarly, knight's swords (also called hand-and-a-half swords, longswords, or broadswords depending on who you talk to. Classifications are largely arbitrary in how they differentiate these types although grip length is a good indicator in my opinion) in Europe were effective against lightly armored opponents, or when used to strike unarmored areas. In Europe, the sword was also a status symbol, with religious and chivalric connotations.

You really need to be a little more specific in your question if you want a useful answer of any sort. There are dozens of styles of two handed sword combat in Europe alone. Asian two handed swords present a range of martial arts uses and battlefield possibilities. That being said, in most of the world, for most of history, swords have been more useful in personal combat rather than on the battlefield. Polearms and shock weapons have largely dominated battlefield melees. There are of course exceptions to this rule, but in general swords are sidearms meant for personal combat. Yes, no-dachi and claymores can take down a horse, but most armies prefer the simpler and safer method of just using a spear. Yes you can kill a man in full armor with just a sword, but a nice heavy mace does it much more easily.

Sources:

Fiori dei Liberi's The Flower of Battle (my teachers have a translated copy, not sure where to get one though)

Nürnberger Handschrift GNM 3227a (German Longsword, this I mostly have just seen pictures from, then learned a lot of it second-hand)

Chuck Wills's The Illustrated History of Weaponry

And a bunch of lectures and lessons from various combat instructors with Art of Combat, Society of American Fight Directors, and Nordic Stage Fight, all of which are of dubious historical accuracy