So that’s how you land a one-ton, car-sized, nuclear-powered rover on a planet 150 million miles away. And oh, one other thing? Because of the 28 minute round-trip for radio signals between Mars and Earth, this all had to be done automatically, with no human intervention whatsoever. We could only sit back and wait to hear word of our success or the deafening silence which would indicate failure. Guided entry, parachute descent, powered descent, and an honest-to-goodness hovering sky crane, all pre-programmed to be able to handle anything an inhospitable foreign planet could throw at us.
In this case the Mars rover is powered by a RAD750, a single-board computer (motherboard, RAM, ROM, and CPU) produced by BAE. The RAD750 has been on the market for more than 10 years, and it’s currently one of the most popular on-board computers for spacecraft. In Curiosity’s case, the CPU is a PowerPC 750 (PowerPC G3 in Mac nomenclature) clocked at around 200MHz — which might seem slow, but it’s still hundreds of times faster than, say, the Apollo Guidance Computer used in the first Moon landings. Also on the motherboard are 256MB of DRAM, and 2GB of flash storage — which will be used to store video and scientific data before transmission to Earth.
See also: xkcd.
You are right that the processor does feel acient. Our current smarthphones are more powerful. The reasoning for this is three-fold. First of all, the computer was selected about 8 years ago, so we have the latest and greated space certified parts that existed then. Second of all, it was the most rubost and proven space grade processor at that time. Thirdly, in order to make a processor radiation hardened it requires lots of tricks on the silicon that is not conducive to making it fast. Given that, it does not run any GUIs and can just focus on raw programming, and actually gets a lot done. All of the programming is done in C, and our toolchain is very similar to programming on any platform.