Depth of Field in photography is how much of a picture is in focus. for example if just the main subject is in focus, (like portrait mode) or if everything is in relatively the same focus. Aperture is what controls DOF by how open the lens is. If it has a wider opening, then it allows more light in which creates a shallower DOF. if it has a smaller opening it would have a larger DOF. A photographer should use DOF to their advantage because if they want to have just 1 thing that is obviously the main subject in the picture, then they should use a wider opening, so they have a shallower DOF and can focus on that subject. If they are taking pictures of a group or a landscape, they will probably want a smaller aperture so the whole picture is in focus.
All of the images above are being affected by aperture because the smaller aperture number, the smaller DOF and the less that is in focus. so the bigger the aperture number, the larger DOF and more is in focus.
SMALL DOF IMAGES:
The first picture above is the featured image because I like the way the blue gives contrast to all the green in the picture. It helps it stand out more as well as the small DOF.