At its most basic, focal length dictates the visual distance between the subject and the camera. Wide angle lenses allow a great deal of the scene to fit in and telephoto lenses allow isolation of certain elements in a scene by magnifying it.
Beyond the perception of how close or far away something appears, focal length also influences the focal plane that the lens depicts.
In photography, the focal plane is a perpendicular surface that passes through the focal point. The shorter the focal length, the wider the focal plane. The closer the distance to the subject from the lens, the narrower the plane.
In addition to focal length influencing the depth of a focal plane, the aperture also affects it. Smaller apertures increase the depth of the plane while larger apertures reduce it.
If you’re shooting close-up macro photography, selecting a smaller aperture will allow more of the subject to remain in focus.
Lenses with longer focal lengths tend to compress the scene, making objects appear closer together. Shorter focal lengths, conversely, expand the scene and exaggerate the distance between objects.
In the example above, the office buildings in the distance are only a block away from Cloud Gate, but appear further due to the distortion wide angle lenses introduce.