Flat in this context doesn't mean 2 dimensional, flat means the universe is not curved, or in other words, it obeys Euclidean geometry. Euclidean geometry is the geometry that everyone is most familiar with and is most applicable in our daily lives. It's where parallel lines never meet and the sum of the angles in a triangle is always 180 degrees. There are other types of geometry where these things are not true. For example, the surface of a sphere is not Euclidean - parallel lines will always meet and the sum of angles in a triangle can be more that 180 degrees.