Why use ground in oscilloscopes and what's the difference between it and a volte meter?
As Alex mentioned, a 'scope is just a fast, graphical voltmeter.  This concept is a bit easier to understand in an old, analog, CRT-based 'scope.  They have a timing circuit that moves a single dot across the screen at a certain (adjustable and very precise) rate, while a completely separate circuit uses the input voltage to move the dot vertically.  Persistence of vision completes the effect.

As a side-effect of this design, which has equivalent tradeoffs in the digital world also, oscilloscopes tend to be optimized for speed over accuracy.  They're usually pretty good, but considering that even a good digital 'scope may only have 256 possible values to display, it's pretty clear that a 3- or 4-digit DMM has a pretty good chance at being more accurate than a 'scope, especially if it's been calibrated recently.

As for the grounding question, the voltmeter does have an equivalent connection.  We just call it the negative probe.  In a 'scope, the negatives are shared between channels and usually connected to the ground pin of the power plug, so you need to be a bit more careful with it, but it serves the same purpose otherwise.