A feather looks like a transparent crack - which is what it is. In some cases, there is some extraneous material "in" the crack, so it becomes greyish or blackish, or the fracture has a complicated shape and it really looks like a bird's feather. All this with a loupe.
As to what it does visually, "Nothing" is probably the closest - as long as size, position and colour of the stone cooperate a bit.
This is an I1 where the grade setting inclusion is a feather - you can see it at about 10 o'clock. I can assure you that it is totally invisible in person (I bought it a few months ago, and DW wears it often).
Here is a VS2 where the grade setting inclusion is also a feather. I can't see it in the photo, and I have great difficulty in finding it with a loupe, despite having a plot and the stone being E colour
And finally, here is an emerald with a huge feather; it nearly crosses the whole stone, which is not uncommon (although dangerous) in emeralds. This is easy to spot with a loupe, but not all that easy to see with the naked eye, and you can see it in the photo as a veil in the stone going N-S. Some smaller feathers are also visible in the NW corner, and one goes at 90 degrees to the largest. BTW, this is a very clean stone for emerald standards.
Apologies it's slightly out-of-focus, but I cannot get the camera to focus properly on this ring.
This is what it looks like on the hand (and even this image is about 2x larger than real life) - you can see the feathering in the corner (which is now SW, and turned by 90 degrees compared to the first image) as a place where the stone is lighter. This is about as bad as it gets IRL, and bear in mind here's it's a still image. If I were to post a video, this would last 1/20 of a second, and then it would blend in with the other reflections.