The Raspberry Pi is a low cost, credit-card sized computer that plugs into a computer monitor or TV and uses a standard keyboard and mouse. Many if not most people have enough cables, cords, mice, keyboards and adapters lying around to get a Raspberry Pi up and running out of the box without having to buy anything else but I definitely recommend paying extra for a kit.
In addition to the Raspberry Pi itself you need a mouse, a keyboard, a WiFi dongle or an ethernet cable (one or the other), a MicroSD Card (Raspberry Pi 2 or higher) and also a Micro SD Adapter (anything lower than a Raspberry Pi 2). You’ll also need an HDMI Cable (assuming you own a TV/Monitor built recently enough to have an HDMI Port, a 5V Micro USB Charger. That’s it, unless you want to play video games in which case you’ll need a USB Controller. Again, you can just pay extra to get (almost) everything in a single kit.
One of the neatest things about the Raspberry Pi is that the hard-drive/operating system is normally housed on a MicroSD card which means you can easily swap out the hard drive/operating system on the fly just by carrying around an extra MicroSD Card.
At the moment I have one Raspberry Pi 2 with several MicroSD Cards. The first SD Card turns my Raspberry Pi into a Retro Gaming Console (glad I didn’t have one of these in college), the second one turns it into a Media Center (kind of wish I did have one of these in college) and the third one turns it into a plain old computer.
And keep in mind I’m not being very creative here; there’s tons of other things you can do with a Raspberry Pi and as is often the case with DIY projects YouTube is your best friend.