The rules changed after there was a judging scandal at the 2002 Olympics in Salt Lake City in the pairs event. Following this, it was decided that there needs to be more transparency and clarity in judging.
The technical score because the element score where all elements (jumps, spins, step sequences, dance segments) are scored separately. Each element is assigned a level of difficulty (jumps are exception). For instance a level two spin will have 8 revolutions in a difficult position while a level one spin will only have one of these feature. This is called by a technical panel of three people. Each called element is then judged on execution by the main panel of judges. For instance, an exceptionally high jump with a difficult entry and exit would bring more points than a jump landed on two legs from a standard entry.
The second score are the components. These are judged on a scale of 0-10. There are 5 components (skating skills, transitions, performance, choreography, interpretation). This works like the old 6.0 system in that most judges probably use it as a ranking device (although there are guidelines on how to mark components). These are later multiplied by a weight (factor) and added to the element score. In men free skate at the Olympics all components have weight of 2 which means that skaters could obtain a maximum of 100 points here. In the short programme the weight was 1 so the maximum was 50. Ladies have lower weights. These weights were chosen such that skaters should care not only about doing the elements but also about the overall quality. In dance the weights are different for different components.