Cut a sheet of paper, so that the sheet of paper is the same size as one of the faces of your cube.
Place the sheet of paper next to the cube. Point at the piece of paper and say something like: "This paper represents a two-dimensional object." Then point at the cube and say: "This cube is a three-dimensional object."
Read, to your learner, the definition for a two-dimensional object. A two-dimensional object has "the dimensions of height and width only." Ask your learner to talk about why the paper possesses only the dimensions of height and width. You might need to hold your paper up while discussing this.
Read the definition for a three-dimensional object. A three-dimensional object has or seems to have "the dimension of depth as well as width and height." Ask your learner to talk about the three dimensions of the cube.
Ask your learner to discuss how the cube and the paper differ in their number of dimensions.
Walk through your neighborhood, home or classroom. Point out those objects that meet the criteria for two-dimensionality (pictures or some patterns, for example). Additionally, point out those objects that meet the criteria for three-dimensionality (chairs and cars, for example).