Let's get one thing straight right now: The title of this entry is NOT a question. It's the actual name of the Demo Disc that I'm talking about today.
Now then...
What's Shenmue is essentially the Japanese Demo Disc of Shenmue for the Dreamcast. It allows you to walk around a portion of Dobuita (The main game's central hub area of sorts), but it actually has you following a goal: You have to find the Head Managing Director of Sega, Hidekazu Yukawa, and ask him what Shenmue is.
To track him down, you need to ask the people around town about him. Most people are clueless, or just don't have time to talk to you. That being said, you'll eventually hit a QTE (Quick Time Event, which is a series of timed button presses) that leads you to the local Arcade. Once you go there, you'll receive Yukawa's Business Card from the Arcade's Manager, which conveniently has the time and place that Yukawa will be written on the back of it.
Once the In-Game Clock rolls around to 4 PM, you have to go to one of the two travel agencies in town to find him. As you enter the building, Yukawa is leaving. He will freak out and run away from you, leading you into another, much longer, QTE. Once you finally catch up to him, he will explain just what Shenmue is. You are then treated to a Cutscene, which reveals that the whole thing was just a dream that Yukawa was having.
Despite being short (It's a Demo, damn it!), it features some NPCs and a few elements that didn't make it to the final game, which is pretty neat. The disc itself also comes with a card advertising a song that doesn't appear to be in the final product.
If you feel like trying something different, and getting a little more out of the small Shenmue Series, I recommend this. I also recommend a Walkthrough if you can't read Japanese, which can be found on GameFAQs.