It is because you're only creating two td elements and 2 text nodes.

Creating all nodes in a loop

Recreate the nodes inside your loop:

var tablearea = document.getElementById('tablearea'),
    table = document.createElement('table');

for (var i = 1; i < 4; i++) {
    var tr = document.createElement('tr');

    tr.appendChild( document.createElement('td') );
    tr.appendChild( document.createElement('td') );

    tr.cells[0].appendChild( document.createTextNode('Text1') )
    tr.cells[1].appendChild( document.createTextNode('Text2') );

    table.appendChild(tr);
}

tablearea.appendChild(table);

Creating then cloning in a loop

Create them beforehand, and clone them inside the loop:

var tablearea = document.getElementById('tablearea'),
    table = document.createElement('table'),
    tr = document.createElement('tr');

tr.appendChild( document.createElement('td') );
tr.appendChild( document.createElement('td') );

tr.cells[0].appendChild( document.createTextNode('Text1') )
tr.cells[1].appendChild( document.createTextNode('Text2') );

for (var i = 1; i < 4; i++) {
    table.appendChild(tr.cloneNode( true ));
}

tablearea.appendChild(table);

Table factory with text string

Make a table factory:

function populateTable(table, rows, cells, content) {
    if (!table) table = document.createElement('table');
    for (var i = 0; i < rows; ++i) {
        var row = document.createElement('tr');
        for (var j = 0; j < cells; ++j) {
            row.appendChild(document.createElement('td'));
            row.cells[j].appendChild(document.createTextNode(content + (j + 1)));
        }
        table.appendChild(row);
    }
    return table;
}

And use it like this:

document.getElementById('tablearea')
        .appendChild( populateTable(null, 3, 2, "Text") );

Table factory with text string or callback

The factory could easily be modified to accept a function as well for the fourth argument in order to populate the content of each cell in a more dynamic manner.

function populateTable(table, rows, cells, content) {
    var is_func = (typeof content === 'function');
    if (!table) table = document.createElement('table');
    for (var i = 0; i < rows; ++i) {
        var row = document.createElement('tr');
        for (var j = 0; j < cells; ++j) {
            row.appendChild(document.createElement('td'));
            var text = !is_func ? (content + '') : content(table, i, j);
            row.cells[j].appendChild(document.createTextNode(text));
        }
        table.appendChild(row);
    }
    return table;
}

Used like this:

document.getElementById('tablearea')
        .appendChild(populateTable(null, 3, 2, function(t, r, c) {
                        return ' row: ' + r + ', cell: ' + c;
                     })
        );