object[][]is the designation for an array of arrays. The second object[,]is a two-dimensional array.
The main difference is that the first can contain different internal "arrays", the second must be rectangular (for example, 4x7).
Example:
int[][] a = new int[] { new int[]{ 1, 2 }, new int[]{ 3, 4, 5, 6, 7 }};
int[,] b = new int[,] { { 1, 2 }, { 3, 4 }, { 5, 6 }, { 7, 8 } };
This is the official guide.
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