The basic components of a personal computer are more or less the same today as they were in the 1990s. Well, perhaps "less" rather than "more." Parts still perform the same overall functions as they once did. The motherboard still serves as the computer's central hub, with everything connecting to it; the processor still follows instructions; RAM still stores data for quick access, and hard drives still store data long-term. The way those pieces are connected and how quickly they operate has changed tremendously, however.
Many people who talk about improvements in computers reference Moore's Law, which essentially states the number of integrated circuits in microprocessors will double within every two years. The more integrated circuits, or transistors, a chip has, the faster it's going to be. But that's only one thing that makes computers faster and better. For example, the magnetic storage of hard drive disks has increased tremendously since the 1990s. We measure drives in terabytes when we used to measure them in megabytes. New interfaces for transmitting data also make a big difference. The Parallel ATA systems topped out at a speed of 133 MB per second, while Serial ATA, or SATA, currently supports up to 6 gigabits per second (768 megabytes).
Recently, computers have begun to use solid state or flash memory technology to store data instead of hard drives, enabling computers to access data even faster. Since the rise of the smartphone, computer hardware has gotten smaller than ever. But even in the smartphone space, a lot of the same components are doing the same jobs they do in full-size computers.