A zanpaku-to is the direct reflection of the power of its wielder, a shinigami's spiritual pressure given physical form. While they mostly look like any other katana an old-time samurai might carry around, zanpaku-to are far from normal. The foremost difference is the ability of zanpaku-to to harm shinigami. Since shinigami are really a kind of ghost, normal blades and weapons can't touch them. In fact, "zanpaku-to" literally means "soul cutting sword."
The other major point that separates them from plain ol' swords is a zanpaku-to's ability to transform. Each blade has up to three distinct forms which its wielder can acces according to their strength and skill. The first, and one that doesn't take any effort to attain, is the blade's normal form. With a few exceptions, a zanpaku-to's normal form is indistinguishable from that of a plain katana.
The second form is called "Shikai", or "first release". The key to Shikai is learning the zanpaku-to's name. Discovering it is not the easiest thing in the world; some Shinigami never do manage it. But for those that do, they gain a whole new level of power. Easily triggered by an incantation unique to each sword, a shikai zanpaku-to changes immensely, often becoming a weapon far removed from a sword. Also, shikai zanpaku-to usually have special powers a shinigami can use, such as poisons, illusions or power blasts.
"Bankai", the third form, means "all release". Only shinigami at the Captain's rank, or highly powerful Vice-Captains can acquire bankai. Increasing the zanpaku-to's power by as much as a factor of ten, it takes many decades of intense training to learn bankai (or three days of cheating courtesy of Urahara and Yoruichi. ^^) Triggering a zanpaku-to's bankai needs only a one-word incantation: Bankai.
Bankai zanpaku-to get additions to their names, indicating it is New and Special, and it changes even more drastically, usually (presently with only 1 exception) becoming something far, far larger than the wielder.
Yeah go watch bleach!