A bokuto is another name for what is often called a bokken. It is a wooden sword used for practicing sparring techniques and physical training with the sword. My knowledge of the Japanese language mostly consists of what I've learned from anime, so I am not particularly qualified to describe the origin of the word.
A book on Japanese sword fighting katas called "Bokken: The Art of the Japanese Sword", by Dave Lowrey says that the terms are equivalent and both mean just "wooden sword".
A bokuto is significantly lighter (and less sharp!) than a steel sword, thus making it a good choice for beginners. Also, a real katana is very expensive, often on the order of 5 grand or so (the cheaper ones you see in catalogs in the US have blades cut with acid, and are usually poorly balanced).
There are many different martial arts which have (or consist almost entirely of) sword forms, including Kendo, Iaido, and Wing Chun. There are also quite a few schools devoted exclusively to sword fighting techniques. One of these (and the only one I am really familiar with) is the School of Two Skies, the method of sword fighting designed by Miyamoto Musashi. In this school, one holds a long sword (katana) in one hand, and a short sword (wakazashi) in another.
At first, it is very difficult to effectively wield a long sword in one hand (or two hands for that matter); Musashi himself notes this in The Book of Five Rings, and so it is useful to have something a bit less dangerous to practice with, as it takes quite a while to get used to striking with only one hand. I've been practicing with one for quite some time now (over 6 months), and every once in a while I still do something which would result in a quick and painful death for me, were I holding a real sword.
Some of the styles only use the bokuto for training purposes, and for competitions, shinai are used. It is my semi-informed opinion that a bokuto is better, primarily because the shinai's lightness encourages the bearer to hit wildly, rather than making a calm, measured strike.