Mathematical approach
Space is a three dimensional world, in which we are limited to length, width, and height, and we can only travel along three perpendicular paths. Mathematicians define a three dimensional space by establishing the x, the y and the z- axis. The fourth dimension would be time, as many people suggest, thereby referring to Einstein's theory of relativation. But we think it's not time but...

Fourth dimension created by vibrations/frequencies
The difficulty with time is that it does not tell us anything about our position. We have to figure out what would be the fourth dimensional axis. We think our state of mind & heart (feelings and thoughts) reflected by our vibrations on the different chakra levels is the fourth dimension. Imagine your being a little depressed because of the lack of understanding that your family has shown to you. Your state of mind & heart is connected to this very thought and feeling, vibrating at chakra level four. Suddenly you receive a phone call from a very good friend, who invites you to a concert of your favorite music group. What happens now? Your state of mind changes, love enters your heart and you visualize the concert with your sixth chakra. So, being at the same place three dimensionally, a feeling about something disappears in an instant, and a new feeling enters, thereby changing your state of mind&heart. You have moved in the fourth dimensional direction! Think of daydreamers, who are present threedimensionally, but absent in the fourth dimension.

Spiritual meaning of the fourth dimension
The spiritual meaning of the fourth dimension is only a matter of overall frequency/vibration, corresponding to the higher chakra levels, 4-8. So, a person can temporarily vibrate in 4D, after a while his/her overall vibration can decrease to the lower chakra levels, 3D. An organization - as a collective entity - can also vibrate on different chakra levels. However, the larger the organization the slower changes in vibration levels occur. Most organizations still vibrate in 3D, because of hierarchy and bureaucracy manifested by many regulations and laws. Increase of body/mind vibration occurs most effectively on an individual level.

Gateways to cyberlands explaining their perspective of 4D
The fourth Dimension: hypercubes' homepage
http://www.fourthdimension.net