One-dimensional

In computer science, probably the simplest and most commonly used data-structure is the one-dimensional array. A one-dimensional array can be conceptualised as a simple list of values arranged in order in memory, such as this -

1 2 7 6 3 34 2 87

When accessing values from the array, it is usual to provide a) the variable name of the array (one of the main advantages of an array is to allow you to access multiple values from the same variable name, allowing you to group data together) and b) the memory offset from the start of the array. The first value is usually accessed by providing the offset 0, because this will read from the first block of memory (the offset 1 will read the second value, because it will move inwards 1 block).

Multi-dimensional

Things get a bit more complicated with arrays that have more than one dimension, which can be conceptualised as tables, like this -

 | 0  1
-|--------------
0| 1 34
1| 2 12
2| 5 37

The rows are usually referred to as the records, and the columns are the fields. To access this array, you need to supply two offsets, as well as the variable name - an offset for the record, and one for the field. So, the offset 1,2 would access the value 37. Most databases are essentially two-dimensional arrays, which is what you see above in the table.

Things get really complicated with three or four dimensional arrays, which are hard to conceptualise. You can imagine a three dimensional array to be a cube of values, and if anyone can conceptualise a four-dimensional one, I'd like to know.

Three dimensional arrays are used in graphics programs to store 3D co-ordinates, but anything above that is usually of little use to the programmer.