Contouring is giving shape to an area of the face and enhancing the facial structure through makeup. Contouring and highlighting make your facial features stand out more.
By contouring you create an illusion of a shadow around your temples, jaw line, nose, and cheekbones to accentuate your bone structure and slim down your face & nose. It's not supposed to be noticeable -- just a subtle definition. Highlighting is to create artificial light to any bone on your face to make them stand out, like your nose bridge, cupid's bow, cheekbones, and eyebrows. Both of these methods work to make your face look "more attractive." Overall, contouring and highlighting are just ways to make your face look thinner if you have a round face, and make your bone structure look the way you want.
For contouring you can use a bronzer, concealer or foundation that is two-tones darker than your skin underneath your cheekbone to make it look higher and more defined. Always avoid shimmery products; contours are meant to be matte, while highlight is meant to have shimmer. Texture is key.
If you want to watch a tutorial on how to do contour and highlighting properly, this video explains everything excellently: