Raspberry Pi is what’s called a “single-board computer” — a small, and relatively inexpensive device that contains most of what you would expect in a bigger computer. Generally, you can treat a Pi as any other computer — you can connect it to a monitor, attach a keyboard and a mouse, and either plug in Ethernet or connect a WiFi dongle, and then use it to connect to the Internet. You can also think of it as a platform for tinkering — the Pi has general-purpose input/output (GPIO) ports that let you connect sensors, motors, lights, and much more. You can use a Pi to build a small computer — perhaps one that’s not even attached to a keyboard or monitor or anything else — that sits in a corner and runs one specific task. For example, it could be a garage opener. Or it could monitor (and display) the local weather. Or it can run a holiday lights display. Or… well, whatever you are able to build. Raspberry Pis are not powerful — they’re about as fast as a smartphone — but they give you the ability to play with electronics, with operating systems, and fill your world with relatively inexpensive computers that help make your world connected.
All Raspberry Pi devices are pretty bare-bones, and need additional peripherals to be useful. At the very least, they need a power supply: a standard smartphone charger (5V, 1A or more, with a micro-USB connector) will do the trick. They will also need a memory card for storage: a microSD card that’s at least 4GB in size. Beyond this, you may want to connect a keyboard and a mouse; an HDMI display; a WiFi dongle. You may need a USB hub. You may want a case, too.
One important note — not only are these devices less powerful than normal computers you can buy in a store, they also don’t use Intel chips and don’t run Windows. Instead, they use ARM chips, and typically run Linux-based operating systems. While there are still web browsers and office programs, things will work a bit differently.
Hundreds of other single-board computers exist. Most are far less popular than the Raspberry Pi. Some take the idea of a Raspberry Pi and extend it (with more powerful peripherals) or shrink it down in size or cost. Often these are called similar names, like Banana Pi or Orange Pi. Some use very different processors (PINE 64 uses a 64-bit ARM processor; the Intel Galileo uses an Intel x86 processor). Some, like the upcoming C.H.I.P., go for price (it sells for $9, and includes WiFi — though connecting a monitor will cost you extra).
When shopping for a single-board computer, consider software support, too. While some other boards may give you more for the money, they often have fewer users — which means that if you run into something that’s not well supported, you may be on your own in figuring out how to get it to work.