Generally, this tool allows you to select contiguous, one-color areas at one click.
If all done right, you will see marching ants surrounding the selected area.
You will notice that the ants marquee became blue and rectangular. This is called a floating selection, which means that the blob is no longer part of the image layer: it is ready to be moved around.
You always have to make the selection float before resizing it or moving it to another place. This can be done by choosing the Transform (F) tool. If that tool is already selected, choose another tool and then revert back to Transform.
Note that moving floating selections between separate documents is not possible. Use Edit|Cut (Ctrl+X) and Edit|Paste (Ctrl+V) instead.
Let's summarize what we did in a more abstract way.
This means using a selection tool to mark a part of the image and produce some black and white marching ants.
This converts the ants to blue and can be achieved by using the Transform tool.
Move it around, resize it, cut, copy and paste.
All marquees are removed and the selection layer is unified with the image layer.
Note that step 2 is not always necessary. You can still copy a selected part if the selection is not floating, and you can still apply filters to the selection. However, you cannot move the selected parts using your mouse!
Selection masks can be added, subtracted and intersected. Additionally, they can be saved to files and loaded back. (In fact, in the memory they are stored as black and white images, white representing the selected pixels.)
Normally, when you use a selection tool a second time, a completely new selection mask is created. However, by holding down Shift, Ctrl or Shift+Ctrl, you are able to add the new mask to the existing one, subtract it or intersect the two selection masks (as if they were planar sets).