These are arrays of arrays. It only allocated space for each array assigned to it.

// allocate memory
int jagged[][] = new int[2][];
jagged[0] = new int[20];
jagged[1] = new int[10];
 
// use array
jagged[0][2] = 15;

These are arrays with more than one dimension. Memory gets allocated for the entire reserved space specified by dimensions.

// allocate memory
int array[,] = new int[2][10];
 
// use array
array[0,2] = 15;

When traversing an array using loops, for example, there are a couple of ways to do it:

// Single Dimension
int SingleDimArr[] = new int[10];
for (int i = 0; i < SingleDimArr.Length; i++) // rows
{
    SingleDimArr[i, 0] = 0;
}
 
// Multi-dimensions
int DoubleDimArr[,] = new int[2,10];
for (int i = 0; i < DoubleDimArr.GetLength(0); i++) // rows
{
    for (int j = 0; j < DoubleDimArr.GetLength(1); j++)  // columns
    {
        DoubleDimArr[i, j] = 0;
    }
}

Alternatively, you can traverse without knowing dimensions if you simply need the array values:

int[,] arr = new int[,] {{1,2,3}, {4,5,6}, {7,8,9}, {10,11,12}};
foreach(int a[] in arr)
{
  foreach(int i in a)
  {
    Console.WriteLine(i);
  }
}

• C# Tutorial: Lesson 2: Arrays
• MSND: Arrays Tutorial