The iMac was generally percepted as an example of good design, while in those days poor design was common for consumer-level computers.

The design team was headed by Jonathan Ive, a bloke that came from the London design firm Tangerine where he spent three years designing bath tubs, washing basins, tooth brushes and the like. He became head of design when Bob Brunner left this position, frustrated as he was with the creative dip that the company was in. Things only started to change when Steve Jobs came back as interim-CEO-for-life.
The problem was not really that there was no creativity at Apple, but more that the nice ideas never made it to the final products. The basic shape of the iMac as well as the color were in design long before steve jobs came back, but the apple board didn't think consumers could handle brightly colored machines (thanks to xunker for this info).

The iMac changed -for a specific part of the market- the criteria on which a computer was evaluated. Coming from grey boxes, that obviously had poor design and only touted their GigaBytes and MHz-en, here was a computer that appealed as a design object. So, Apple was able to sell -and sell well- a less compatible product, that was slower than the competition (although fast enough) and had a unsharp and small screen.

Jobs made it possible that for once the designers could tell the engineers what to do. Usually, it's the other way around.

In designing the iMac, the team faced many problems. In fact, to get the transparency right (and homogenous), they got help from a firm specialised in the coloring of candy.
Another issue was that the transparency revealed the innards of the system. So, the PCBs of the motherboard, mouse etc. had to be engineered both from an electronical and from a design perspective. And then there is the mouse ball, which has two colours so you can see it rolling. That said, the hockey-puck-like mouse of the early iMacs was not their most popular part.

In addition to sheer looks, the team also managed to keep the iMac small, cool, lightweight and silent. The motherboard had more in common with a laptop-motherboard then with that of a plain PC.

A post on Slashdot said something about the iMac being designed by Gingko Design. I don't know whether this is true, but it's a solid fact that John Ive was an Apple employee at the time. The Gingko portfolio shows some nifty designs though, so it could be possible.

UPDATE: the new TFT iMac continues the tradition: it is a small, silent, expensive (and not top-performing) computer, only this time it does have a decent screen. And it is no longer a single fixed unit - the screen is now attached to the base in a flexible way so you can move it in any position you like. This design was apparently inspired by the shape of an angle-poise desk lamp, where the previous iMac is said to be inspired by the shape of a gum drop.