The SDK is the developer's kit that you can download from Google. It contains a number of tools for use in developing applications for the platform, among them an emulator (for testing apps as if you're on a real android phone) and the ADB tool for accessing the hardware over a USB connection.
The ADB tool is run on the command line (no graphical interface). That's usually a bash prompt found in any console/konsole/terminal in Linux or by running cmd.exe in Windows. It allows the user to execute standard linux shell commands on the phone's filesystem.
For example, the above command runs adb, tells it to issue the "ls" shell command, which gives a directory file listing (similar to the "dir" command in DOS.
Anything beyond that is above my head as of yet, since I don't have any Android hardware to use the tools on.