What does a line graph in which the data points do not fall along a straight line mean?

There are several possible answers:

The line is actually meant to be a curved line and not a straight line.

The relationship between the two variables is not a linear function.

Discovering this can be one of the main reasons for drawing the graph.

The data points are empirical measurements (from an experiment, for example)

and there are errors associated with the observations. The errors may be systematic

or random.

You have made mistakes - either in recording the data or in plotting them.