Feather

To a soften an edge between a selection and surrounding pixels, we use the option “Feather”.
To use this option, we have a number of possibilities.  One possibility is to use the “Feather” box that we find in the options bar at the top, when a selection tool is selected (1).

A second possibility is to first make a selection, then the “Select” button in the menu bar, choose “Modify” in the drop-down menu and click on “Feather”. This opens a dialog box (2) where you type in a value for the “Feather Radius”.

A third possibility is to first make a selection, the “Select” button in the menu bar and select “Refine Edge” in the drop-down menu.

In the “Feather” (1), give a value for the feather radius.

The later is my preferred way of working. Why?  Because you can see what you’re doing when the “Preview” box (2) is checked.
And because you can preview the selected in different ways (3).

Click the OK button when you are satisfied.

This brings you back into the picture with the selected area, where not much has changed to the selected at the first look.

But when you drag selected into a different image, you will notice that the cover-up is perfectly equal to the obfuscation that we got to see in the preview.

Anti-alias

When we make a selection, we find the option “Anti-Alias”, not always but in most cases, in the top option bar and we select this.

What this option does is, it makes the edges of the selected area smoother.
To clarify this, I have two selections, an alias and an anti-alias and I will make a channel of these selections.

For this I click the “Save Selection as Channel” button (1) from the bottom of the “Channels” panel.

When you zoom in the picture and view these alpha channels (2), you can clearly see the difference between the area selected with and without Anti-alias.

Alias gives a more rough selection, while Anti-aliasing has a more smoother transition between the selected and unselected.

FYI, the black pixels in the alpha channel are not selected pixels, the white pixels are the selected pixels.

The Alias selected area has only black and white pixels, while the Anti-alias selected area also has pixels with different gray values.

It is these gray values that ensure the smooth transition.  The lighter the gray value, the more transparent the pixel.

FYI.
When you view the alpha channel of a selection where you have “refined edges”, you will see that there are several differences in the gray values present.

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