What's the goal of Minecraft and what can users achieve in this world?

It's a sandbox - there is no strict goal other than to play around and survive. You can even keep dying all the time if you like, you always respawn, you just lose what you were carrying, so even that is optional! It just provides a set of gameplay mechanics (mining and crafting, not surprisingly) that let you muck about, build stuff, discover things, defend yourself, etc. I thought it sounded pointless until I bought it because I was bored and was surprised to find that it's worryingly addictive ;)

At the moment (with beta 1.5) there is no goal beyond surviving, earning a few achievements and what goals the user sets themselves. These might be building a creeper proof house, finding all the gold on the map, exploring the entire world etc. What keeps the game going? Whether the user has met their self imposed goals or not. I have heard that there is meant to be a goal built into the game, but I haven't got a link to it at hand. From my point of view I'm quite happy with the goallessness of the game.

The really cool thing about this game is that it lets you create your own goals. Right now my goal is to grow a giant floating tree fortress.

Multi-player is now just about identical to single player, and there is a real draw in an absolutely free multi-player system with a persistant world. You're not just building this heap of neat buildings, but then other people are walking through them and adding onto them. I have 4-6 really active players on my world and some of the stuff we've built--I look back and it boggles the mind. My brother built most of the train system. It involves a LOT of electronics in order to make it simple to use. you walk in, a cart is sitting there. You get into the cart, press one of 5 buttons on the wall and you are sent off to your destination. Your cart is replaced from a parking lot so there is one ready to go for the next person. A parking system recovers your cart when you return. One player has built a massive citadel he calls "Cloudkeep" that has covered an entire mountain at this point. One lady is extremely artistic, the stuff she does just boggles my mind, I walk through her area every now and then just gazing at the beauty. It's amazing what can be done with 1m square blocks and the right attitude. We have a "Fixer" who tends to run around and beef up lighting (He's great at counting exactly how close torches need to be to avoid monsters spawning) and security in our walled town and in peoples areas. He also helps with the railroad and has made a museum that shows off many redstone circuits for reference. Oh and one guy has create a massive 3-level tree farm that he regularly goes out and cuts down to keep a double-chest in town completely full of wood. it's a great service and he claims to find it relaxing. I keep the town walls safe, help out on projects, have a massive glass factory going (I've actually covered over a huge sand peninsula and converted the entire thing to a giant empty cave that has become a big remote train station and food farm. Get together with friends and give it a try. Remember it's an infinite world (virtually), you don't have to step on each others feet at all--just travel out and find a location that inspires you, then build something. It seems that there is always something new to try.

The shortest answer I can think of is: sense of achievement. Think about other games with linear story lines for a moment. While these games define clear goals for you to obtain in order to reach completion (e.g. "Beat the final boss", "Reach destination x", ...) all of these things could be accomplished just the same if the game had no clearly defined ending. So Minecraft isn't really much different from other games. It doesn't define one single ultimate purpose, but that doesn't mean you can't enjoy the interaction with your environment like you would in linear games. Perhaps Minecraft still isn't a game for you. I'm a pretty big fan of linearity in games myself so Minecraft is an unconventional experience for me as well. I'm just saying the way it seems most people are enjoying Minecraft is by seeing any conceivable task as a goal rather than a means.

While some people are starting to find vanilla Minecraft boring, there are mods, as well as modpacks, such as http://feed-the-beast.com/ and http://www.technicpack.net/ which enhance the gaming experience. Some mods add computers, which feature actual programming languages, others include more functionality with redstone for the logical thinkers. Essentially, anything can be made into a mod and implemented, altering the experience. Some people like it incredibly challenging, so they get a mod like http://forum.industrial-craft.net/index.php?page=Thread&threadID=7156, which makes things incredibly hard to craft. Some people like the concept of bees, and there is Forestry for that. The goal and what is achievable is totally up to you and whatever you make of the world. You could make an incredible structure, or you can make an industrial type city, which makes everything easier. You could capture mobs and make fun ways to kill them. It's all up to you.

Minecraft doesn't HAVE point really. You just do, well, anything! You can play creative or survival, which ever you prefer! Creative- Un-limited supply or blocks and flying. Flying makes it easier to build sense you can reach anywhere. And Mobs still spawn but, can't hurt you. Which I love! Survival- Gathering resources to help you survive your world. I like to pretend the world is having a zombie apocalypse! As for mobs, they spawn and can hurt you. And those are an overview of the two game modes!