Have you read this:

http://processing.org/reference/Array.html

An array is just a list of things - variables or objects. For example if you had 1000 height measurements you could store them in an array of floating point numbers.

float[] heights = new float[1000];

means make me an array of floats, length 1000. Once you have put the values in the array you can then refer to them by the index number (which ranges from 0 to 999).

heights[0] is the first value. heights[56] is the 57th value....and so on.

Yep, here's a sketch I wrote which uses arrays to hold the positions and speeds of the particles:

http://www.openprocessing.org/visuals/?visualID=6407

In effect, nothing. But in the case of 1000 of them you would have to use 1000 lines defining them all, and then think of 1000 different names. And then when you wanted to do something to all 1000 of them... again, another 1000 lines of code.....

Or, using an array, to multiply all numbers by 2:

for(int i=0; i<1000; i++)
{
   numbers[i] = numbers[i] * 2;
}