The Bo-Hi is a groove on the blade lengthwise. It reduces the weight of the Katana without weakening the strength of the blade. It also shifts the balance point of the Katana slightly towards the Tsuba. This makes the sword slightly faster and lighter in its cuts.
This groove also has a very practical advantage for those who do martial arts like IAIDO, in fact it allows a rather special sound that helps to recognize a good cut by slicing the air.
All about the Bo-Hi
You may have heard that this groove was also historically intended to draw the opponent's blood all the way through, but this is actually a myth.
There are several variations of the Bo-Hi, the most classic is the one that ends at the Habaki, but some grooves are just halfway down the blade or at the beginning. These variants have more of a visual purpose than a practical one.
Some craftsmen hollow out the Bo-Hi in combination with the Kissaki shape to make it visually perfect, but this is quite rare nowadays. You can find this on high end or antique.