The Raspberry Pi B/B+ is a mini-computer:
- plug a mouse and keyboard into the USB ports,
- attach a monitor or TV to the HDMI port,
- insert a micro SD card with Raspbian,
Internet access can be via the built-in Ethernet port, or you can plug a wifi dongle into one of the USB ports.
There are several models and versions available. The first generation has models A, B, and B+. The second generation so far has just an upgrade for B. If you don't have a Pi yet, the Raspberry Pi 2 model B is very much recommended.
A Raspberry Pi comes without any other hardware, so there are some extras you'll need to gather. You might have some of these lying around, or you could buy a starter kit that has most of these included:
- A micro SD card of at least 4GB and a decent speed (like class 10)
- A micro SD card reader. Some computers (especially laptops) come with an SD card reader. With a micro SD card adapter you can use it to read & write micro SD cards. Alternatively, you can buy a USB micro SD reader.
- A 5V power adaptor to power your Pi (at least 1000-1200 mA)
- An HDMI cable to connect a monitor to your Pi*
- A USB keyboard and mouse you can spare for a few minutes*
- If you want to connect to your wifi instead of via a cable, a wifi dongle
- And if you want to fit your Pi in a nice case, you'll find plenty of options in various online shops (or you can 3D print one)
A micro SD USB reader, a micro SD adapter, and an SD card slot in a laptop.
Assuming you have a Windows computer, there are a few (free) programs you'll need:
- Win32 Disk Imager, a free tool you can use to write to and read from a (micro) SD card.
- MobaXterm, a free terminal program that lets you connect to your Pi from your computer.
- The latest Raspbian image, the OS of choice for your Pi.
Mac Alternatives (I don't have a Mac so I can't recommend any):
Setting up a new Raspberry PiRaspberry Pi - First Time Configuration