Hi, CVaughn, and welcome.
I had hoped that Mark would have visited the forum to answer you, and I hope he still does, but I will already try to give you an answer.

As you know, the images that you see on your monitor are a mosaic of pixels (picture elements). If you want to change the information (this is the colour and the brightness) of a pixel, you have to tell Photoshop (or any other app) which one you mean. Therefore you select this pixel, or this group of pixels and then you do something with it (them). Feathering a selection does not do anything with the pixels, but gives Photoshop a command like: "Whatever I do, you have to apply 100% to the central pixels, but at the borders you have to diminish the influence and take into account the information (colour, brightness) that is already there."

Practically speaking, Photoshop was waiting for your orders what it had to do with this selection with a feathered outline. You might for example invert the selection and then , as is suggested, take your erazor and eraze all that is not selected. If you click on the eye icon of the (background) layer under it so as to make this layer invisible, you will see the borders disappear.

But this is only half the story. Ready?
The selection outline, aka the marching ants, does not show the border of a feathered selection, but halfway between full strength and nothingness. To understand this, you'd have to use a mask, but more on this later. Let's not make it too complicated right now.

Practically speaking: if you imagine your feathering as a gradient going from black to white, the marching ants show you middle grey. So your selection would fall off halfway.

Therefore you may want to do the following:

1/Open your background image.
2/Open your photograph, select the arrow tool (upper right hand corner on the tools palette) and drag your photograph on the background image. You will notice that it is placed automatically on a new layer.
3/Be shure that this layer is selected (its name is coloured. Now Hold Ctrl down and click on its name in the layers palette. Your photograph is automatically selected.
4/Go to Select>Modify>Contract and fill in a number like 10. (you may change this. The higher the number, the smoother the transition). You'll notice that your selection becomes smaller.
5/We saw that the marching ants are halfway the feathering-to-come, so enter a number for feathering that is the double of the contract number, in this case, 20.
Now your selection really ends at the edge of your image and you will have a fall-off of twenty pixels.
6/But in fact, what you want is not to do something with the photograph, but with the edges. Therefore you choose Select>Invert. You'll see now marching ants where they were before, but also at the border of the photo.
7/Now click on the eye-icon of the background layer to make this layer invisible and take your erazor tool. Select a big one, 100 or even bigger and fearlessly eraze all your image. You'll see that only the borders are erazed, and the closer to your photo, the less you can eraze. You have a softened border.
8/ Make the background visible again and flatten.


Try this out, and a next time, we'll talk about masks which are the opposite of selections, but are far more handy to work with.

If you don't work against time, time often works for you.