Excel expects the data series to be organized in columns. Your data table should really have the x-axis values (Months) in the first column, and the y-axis values for each data series in subsequent columns.
BUT Excel has a shortcut to remedy this problem. Click on the graph to select it, and choose Source Data... from the Chart menu. Then click on the Switch Row/Column button.
That should fix it.
You could also transpose your data, and then re-create the graph. This is easily done using Paste Special. First, select all of your data, including headings, and choose Copy (or CTRL-C). Click in a cell to the right of your data (where there is enough space to hold the transposed data, and then choose Paste Special... from the Edit menu. Check the Transpose option and click OK.
If you re-make your graph using this transposed data, it should be organized the way you want it to be.