string[][]
is not a two-dimensional array, it's an array of arrays (a jagged array). That's something different.
To declare a two-dimensional array, use this syntax:
string[,] tablero = new string[3, 3];
If you really want a jagged array, you need to initialize it like this:
string[][] tablero = new string[][] { new string[3],
new string[3],
new string[3] };