The term “supercomputer” is a time dependent term and refers to the class of most powerful computer systems worldwide at the time of reference. In any case this is the most practical definition. In the scientific realm these machines are comparable with large-scale scientific facilities (e.g. large telescopes) that enable “big science”. Supercomputers are typically used when tackling large-scale compute problems that accompany some scientific/technical research. The most obvious example is weather predictions as almost everyone appreciates the time pressure put on the calculations in order to prevent that the predictions are overtaken by the actual weather.
There are more research areas in which computations play a significant role. The facilities for large-scale computations are often necessary compulsory conditions to conduct successful research. The computational load is sometimes so large that the speed of the computers determines if the work can be realistically undertaken. In other work the aspect of time can be significant too. Some (computational) work has to be done in pace with experimental work and for efficient research too large a time gap must be avoided.
The speed of (super)computers is expressed in flop/s, floating point operations per second; nowadays mostly in the form of Gflop/s (10^6 flop/s) and Tflop/s (10^12 flop/s).
In spite of (or thanks to) the advanced technology applied in supercomputers, working such machines is often not more cumbersome than working with a couple of PCs. Also access does in general not pose a problem.