Flatland describes simple principles of geometry and dimension, In detail it deals with 1st, 2nd and 3rd dimension.  Also suggests about the possibilities of existence of 4th dimension(time) which was unknown of  at the time of release of the book.

To understand this as a scientific matter i found some information on dimensions  and hypercube. This illustration explains 4 dimensions of a cube.

"4 Dimensions of Cube" taken from http://en.wikipedia.org/wiki/Hypercube

0 – A point is a hypercube of dimension zero.

1 – If one moves this point one unit length, it will sweep out a line segment, which is a unit hypercube of dimension one.

2 – If one moves this line segment its length in a perpendicular direction from itself; it sweeps out a 2-dimensional square.

3 – If one moves the square one unit length in the direction perpendicular to the plane it lies on, it will generate a 3-dimensional cube.

4 – If one moves the cube one unit length into the fourth dimension, it generates a 4-dimensional unit hypercube.

This illustration shows geometrical graphs representing cube in multidimensional space:

"Cube in 12 Geometrical Dimensions" taken from http://en.wikipedia.org/wiki/Hypercube

This animation shows a computer generated model of cube existing in 4 dimensional space which is a hypercube:

Animated Version

To further understand dimensions an how they are formed I looked at the video on YouTube called “10 Dimensions in 10 Minutes” which explains how each dimension forms and what makes it different from previous dimensions. @ (http://www.youtube.com/watch?v=uY_ZgAvXsuw)