The marquee tool targets a specific section of your canvas allowing you to use most tools on that section without altering portions surrounding it.
First click on the Marquee tool and scroll over your image or blank canvas (Blank page, recognized by checkerboard background). Click, and drag over the image to select it. Only this area is now affected by any tools. If you press the delete key now, it will only delete that area and if you use the copy or cut tools, only that area will be cut or copied. If you right click on the button you will get an option bar with "rectangular Marquee tool" "Elliptical Marquee tool" and "Single row/column" on it. Each of these makes a different shape of selection. At the top of the screen, you will see the "Feather" option. Enter a number of pixels there and it will soften the edge of your selection, which is extremely useful in photo editing, as almost all photos have some level of blur. In most cases these tools will do everything you need them to, but sometimes you will need the lasso tools.