The Raspberry Pi is an ARM based computer, so your usual x86 / x64 software won't run. Also, it was designed to be cheap, not quick - so it may well be slower than your run-of-the-mill smartphone. Still, it is fun to play with, provided you remain reasonable in what you ask of it. It is a fine controller for all kinds of hardware, and will do as a reasonably low-energy server too.
There are two models available, which are essentially the same, except for RAM, number of USB ports and presence of an ethernet port. The model A has 256MB RAM, a single USB port, no ethernet, whereas model B has 512MB RAM (nowadays - the first models were 256MB), two USB ports and an ethernet port. Otherwise, there is the CPU, an SD card slot, an HDMI connector, audio output, a number of GPIO (general purpose I/O) ports - for details, check out http://www.raspberrypi.org. Whatever the model, the documentation insists on a strong enough energy source - it may be standard USB, but should provide a full 1A (ampere), otherwise instability may ensue. It's not just any adapter that will do. Also, depending on USB peripherals, you may still get surprises, so preferrably don't connect just anything to the RasPi.
Depending on what you want to do, you may want to use a more or less large and/or quick SD card. The standard recommendation is “no lower than 2GB”, you may want to use a 4, 16, 32, … GB card.