Multi-dimensional arrays are simply arrays where some/all of the values are other arrays (as opposed to scalar values), sometimes referred to as "an array of arrays". So, if you create an array of scalar values as...
$myArray = array('foo', 'bar');
...then you could instead create an array of arrays as...
$myArray = array(array('foo', 'bar'), array('testing', 1, 2, 3));
In this case, the value of $myArray[0] would be the array with two elements with the values 'foo' and 'bar'. You could therefore reference the value 'bar' as $myArray[0][1].