In his book Making it New, Henry Geldzahler (a big deal), echoing John Szarkowski (another big deal), states that, “The edge is the controlling aesthetic factor [in photography].”
Here are three pictures of the same thing but with different edges.

This first picture most represents what I wanted to take a picture of in that moment: a wilting orange lily in a teacup on my kitchen windowsill. However, this didn’t really give me enough to look at or think about. It is my least favorite picture of the three, even though I initially thought it would be so cool.

In this picture, I still wanted an area of focus to be my orange lily. However, I also wanted to provide slightly more context. This lily is in a teacup that is a part of a row of teacups on my windowsill. In this picture I wanted to provide more of the story, but not the whole story. There is still some mystery. How many teacups are there? Is there another one with a flower in it? Are the teacups identical? What else is there?

This last picture tells the whole of the flower-filled teacup on the window story. That entire portion of the window is in view. We see every part of every teacup. To me, though this picture is the most straightforward, is also the most evocative of the place. I understand more about the room in which this windowsill with teacups and a wilting lily is located. Even though this is the only part of the room I can see. Is that what I was going for originally? No. Is that what is the most interesting to me now? Yes.
The edge can make or break the whole picture in terms of aesthetics, but also in terms of story a picture tells. Though the edges of a picture tell us what is important about what is happening within the picture, they also provide insight into what is left out. Sometimes, what is left out of the picture is the more interesting piece.