The QGIS Python console is a Python console. You can perform all of your normal Python tasks with the added benefit of having the QGIS libraries added. From the console, you can manipulate GIS data and display it on the screen, or not.
The Python console is located under the Plugins menu on the QGIS toolbar. You can also access it by pressing Ctrl + Alt + P on the keyboard. The console will usually open in the bottom of the main window. You can undock it by clicking on the title bar (where it says Python Console), holding down the mouse button, and dragging the window to another location on the screen or by clicking the window button at the top-right of the console:
The console has buttons for clearing the window, importing GIS and QGIS specific libraries, running the current command (you can...