ADB installer1.4.2 - Download

These two tools allow you to send terminal commands to your phone from your computer via USB. They both serve different functions, but they can be installed with relative ease at the same time, so it's helpful to have both. Here's a (very) brief breakdown on what these tools do:

Android Debug Bridge (ADB): This tool allows you to send a wide array of terminal commands including but not limited to basic Linux shell commands, plus some specialty developer commands to your phone at just about any time (as long as you have debugging enabled on your phone). You can send commands while the phone is turned on and booted, or even when it's in recovery mode. While ADB is often used in conjunction with rooting or modifying your phone, you can use ADB to send terminal commands to unrooted devices as well.

Fastboot: When you need to modify your phone's firmware, fastboot is the tool you need. This allows you to send commands to the bootloader, which means you can flash/modify things like custom recoveries. You can't flash whole ROMs with it, but it's helpful for many things that ADB can't do. Fastboot isn't enabled for all phones, so you may have to check your specific device.
Both of these tools come with the Android SDK, however this is an extremely large download that, frankly, most users who are interested in ADB and fastboot don't need. If you just want to root your phone, flash some ROMs, and mess around in the terminal without having to muck about with complex button combinations, skip the SDK. Here's how.