The Gyuto Knife / "Cow Sword"
In simplest terms a "Gyuto knife" is Japanese equivalent of a chefs knife. The most popular knife in the kitchen and the knife that performs all tasks quite well. The term "Gyuto Knife" or "Gyoto Knife" with the Gyuto being slightly more popular (roughly 79% of the time people describe the knife the word "Gyuto" is used) both refer to the same blade.
Typically a Gyuto knife has similar dimensions as a chefs knife, from the bottom of the handle to the tip the distance should be about the same as from your wrist to your elbow. If you're 6 foot tall we are talking around 21cm blade with a handle around 14cm (with 1cm in between meaning 36cm it total - a bit longer than a school ruler.
When compared with a chefs knife you will notice that the steel in the blade handle is shorter and doesn't go right to the end like a western chefs knife. The handle is inserted inside the handle rather than cut the handle in half like a western knife. This means that Japanese Gyuto knives are typically much lighter weight than and chefs knife.
In addition to lighter weight the Gyuto is sought after largely due to it's ability to maintain a crisp, hard edge. This hardened edge originally came from the sword skills of Japanese blacksmiths and is predominately due to increased carbon throughout the knife (iron is in all knives whilst the addition of carbon makes it much harder (up to 1000x times as hard as a wrought iron only knife). The flip side is that carbon can make knives more corrosive so modern Japanese Gyuto knives are now made with a strong high carbon steel down the middle and stainless steel wrapping around on both sides. This allows it's holder to benefit from the best of both worlds.
In terms of purpose, the Gyuto is an all purpose knife. It has a medium width at the belly and a slight curvature to the blade meaning you can chop, slice and roll the knife on vegetables, fruit meat or bread (just don't smash it into the bone).
History & Origin on the Gyuto Knife
The Gyuto knife was invented to adapt to a change in Japanese culture hundreds of years ago when they legally allowed people to eat meat (prior to that the citizens of Japan were not allowed to eat red meat or any animal with more than four legs that it stood or walked on). The name "Gyuto" knife actually meets "Cow sword."
Prior to the Gyuto entering into the market Japanese knives such as the Nakiri knife and Deba knives were more common as they were designed specifically for fish and vegetables - the base of their diet (these knives are still commonly used today inside Japan).
Why choose a Gyuto?
The Japanese Gyuto knife is the most common first knife in a Japanese chefs knife collection. Given it does just about everything you don't actually need any more knives.
That said, it was my first Japanese knife and now I have over 100 knives (and counting) - whilst it can be your only knife it can also start a mild obsession.
Good luck and any questions feel free to ping us :)