Just for additional information, I live in the United States.
The most significant difference between the license levels is that of band access. You can find a list of the various band allocations, with notes on what levels are allowed access, here:
There's also a handy chart of the allocations available here:
Some of the lower license classes also specify a lower maximum power level for certain bands (e.g. Novices are limited to 25W in the 1.25m band).
Note that higher levels of license are still subject to the overall maximum limit - ham radio in the US is limited to 1.5 kW PEP (peak envelope power).
Type of operation
Some of the lower license classes limit the operator to a certain type of operation such as CW (morse code) on certain bands.