Bokken are both training tools and weapons in their own right.
The suburi bokken comes from the legend of Musashi. As the story goes, he was crossing a river on a boat to go to the duel of his life when he realized he didn't have his katana. He fashioned one of the oars into a sword. It was heavy, but Musashi was well renowned for his strength. He, of course, defeated his opponent.
The more traditional bokken was used as a training tool. It hurt when you were hit, but it didn't cut you. It was plain, without grooves, saya (scabard), or tsuba (hand guard). It was used primarily to learn the sword katas for beginners. Newer tools such as the iaito and the shinai replaced its use in more modern times. The iaito looks and feels more like a shinto (new blade/cutter) allowing the student to practice drawing the sword and notto (sheathing the sword). The shinai is used in modern kendo, as it produces fewer injuries.
Some schools still use the bokken, as it has a ha (edge) and mune (back). These features ensure that the waza (techniques) practiced translate better to a proper katana. Modern kendo includes waza that will only work with a shinai.
Outside of the suburi bokken which is studied as its own weapon, and builds strength (it's heavy), all the other variants of bokken are just modern conveniences to fit the tastes of the buyer. The hi (groove) only serves to lighten the weight of the bokken.