For some reason that concept seems to be a difficult one for photographers just starting out or at least it was for me. So let me see if I can explain it simply, and if you have a better way of explaining it, add your comments. I'd love to hear your explanations.
Here goes. Each lens has f-stops. They determine how big the opening is that lets light into the sensor in your camera. Here's the part that drove me crazy when I first started out. The big numbers, like f-22, mean the opening will be small, and the small numbers, like f-2, mean the opening will be big. My brain took awhile to get this concept, but I've got it now.
In order to make the fence disappear, you need to use a small f-stop number, like f-2, which will give you a very narrow depth of field. That means the owl will be sharp and the area in front of him and behind him will be out of focus, which is exactly what we want. Out of focus fence means it will disappear or fade greatly.
Lenses vary, so use the smallest f-stop number you have. Then focus in on the owl or whatever it is behind the fence you want to shoot. Be careful you are not focusing on the fence itself or you will get a lovely shot of a tack sharp fence - not what you want! Hold still and shoot. That's it! It's not rocket science, but it can make for wonderful photos.
Now go forth and make it a day to try something new - like making fences disappear!