I hope everyone has already grasped this concept from previous posts, but I want to give it a try myself.
The number of dimensions is how many values are needed to describe the location of a point.
If your world is a point, no numbers are needed to find something.
If the world is a line, one number can tell you where any point is (relative to somewhere else).
If the world is a plane, two numbers are needed. For instance, to locate a dot on a piece of paper, you might say it’s 2cm from the right edge and 15cm from the top. Another example is latitude and longitude (the surface of a globe is actually 2-dimensional in this sense).
To find a point in space, you need at least 3 numbers. In the globe example, you might expand to a 3D description by including height above or below sea level.
If you take duration into account, you need 4 values to locate an event in space-time.
Other theories of cosmology and quantum gravity require more values to fully describe an event, so some physicists will talk of 10 or more space-time dimensions.
By the way, some systems of mapping don’t use linear dimensions. For instance, it’s not uncommon to see ‘polar’ coordinates that describe distance from the origin and angle above and to the side of some axis. Though the values aren’t Cartesian x, y, and z, there still need to be at least 3 to find a point in space.
So, dimensions aren’t places, they are just values in a mathematical systems.
If you want an entertaining exploration of higher dimensions mixed with a satire of Victorian society, read “Flatland.” Great book.
“If you prick me, do I not–leak?” —Lt. Commander Data