The selection tool allows you to select part of the canvas to move around, transform, and restrict your painting to. Check out Mark's great tutorial for in depth examples.
As you make strokes with Select tool active the mode determines if new areas replace, add to, or subtract from the active selection.
The operations allow you to make changes to the selection path as a whole. Deselect clears the current selection so you can once again draw on the whole canvas. Invert reverse the selection so what was previously unselected becomes the new selection. Expand let's you grow the selection and Contract lets you shrink it. Border selects a thick line around the current selection. Layer selects all the contents of the current layer.