Think of it this way.
When you drive your truck down the road, you see your buddy at the gas station.
You throw the wheel to the left, the truck turns left, but, the right front corner dives in and it tries to throw you into the passenger seat.
the only thing keeping the truck from flipping over is the hard ground it is riding on. Now if you remove the hard ground and put snow under it, then when you throw the wheel to the left the right front corner will dive in.
Now, take nascar. They put huge banks on the corners. This angles the car and changes the angle at which the G-forces are pushing. When you are going straight, the G-forces are pushing your straight down. When you turn left the G-forces are pushing you to right. Thus they "bank" the corners to counter this. If they didn't the cars would have to either slow down or be thrown off the track.
With snowmobiles you have to "create" the bank. That is what carving does. It creates a bank and counters the G-forces trying to push you to the right.
When you "counter" steer what happens.
You want to go left. By turning right you are forcing the left side of the sled down into the snow. Once you achive the proper angle (you will figure this out with practice), you can then start steering into the corner to turn faster, this will also control the angle of the sled so you don't fall over.
As for throttle.
If you are sitting in one spot and just pin the throttle what happens?
Yep, bring chop sticks cause you are digging a hole to china.
Now, what happens when you pull the sled over to say (for example) 45 degrees and hit the throttle?
The track is still trying to dig to china, but now it is digging sideways at a 45 degree angle. As it displaces the snow the back end can "slice, or side if you like" sideways and allow you to turn faster and sharper.
I hope that makes sence.
kind of long winded, but hopefully that explains things at least a little.