You can traverse a two-dimensional array effectively by using nested loops, where you iterate through each row and subsequently through each column.

In a two-dimensional array, data is organized in a tabular structure, consisting of rows and columns. To access a specific element, you must know both its row index and column index. This is where nested loops become particularly useful. The outer loop iterates over the rows, while the inner loop iterates over the columns of each respective row.

Let’s consider a two-dimensional array denoted as ‘arr[][]’, which contains '$m$' rows and '$n$' columns. Here’s how you can iterate through this array using nested loops:

'''java for (int i = 0; i < m; i++) { // Looping over rows for (int j = 0; j < n; j++) { // Looping over columns System.out.println(arr[i][j]); } } '''

In this example, the variable '$i$' serves as the index for the rows, and '$j$' serves as the index for the columns. The outer loop, represented by ‘for (int i = 0; i < m; i++)’, iterates through each row. For each iteration of the outer loop (i.e., for each row), the inner loop ‘for (int j = 0; j < n; j++)’ executes, iterating over each column in the current row. The statement ‘System.out.println(arr[i][j]);’ then outputs the element located at the '$i$'th row and the '$j$'th column.

This method of iteration is referred to as row-major order, which is the most common traversal method used in many programming languages, including Java and Python. Alternatively, you can iterate in column-major order (first by columns and then by rows) by simply swapping the order of the loops.

It is important to note that in most programming languages, array indices start at $0$. Therefore, the loops will run from $0$ to $m-1$ for rows and from $0$ to $n-1$ for columns, respectively. The number of iterations of the inner loop is contingent upon the current iteration of the outer loop, which is why we refer to them as ‘nested loops’.