adb.exe is part of the Android developer toolkit (ADK) that you can download. In fact for plain user (not Android developer), we only need the following 3 files that are usually available in many tools for customed ROM :
You would better download the ADK so you will get the latest version. When you connect the phone either in recovery mode with an USB cable to the PC, the PC has (at least under Win7/Win8) automatically Android adb device driver installed, so it recognizes the phone correctly. By launching adb.exe, you will get to an adb command prompt where you can issue several commands like reboot, restart to recovery, flash the partition etc.... (communication is established between adb.exe in PC and the phone ) You can also issue the su command as far as I remember, then you the the "Linux"-like shell prompt. And dd, ls, du, cat commands of busybox etc... are then all available. You exit the shell by 'exit'.
Searching for adb, fastboot etc.. would help you.
Hope this helps,