Whenever experimental data is being graphed, the 'points' representing values resulting from measurements are never perfectly accurate - there is always some error in measurement, leading to uncertainty as to the exact value. The amount of uncertainty is minimised by careful measurement, but it always exists.
A graph is drawn to show the trend in data. Joining up points in a dot-to-dot fashion ignores the uncertainty in measurement of the results, and obscures the trend. A line (or curve) of best fit should always be drawn so that the trend in the data is emphasized.
A second purpose of many graphs is to allow the formulation of a mathematical description of the relationship being shown - an equation for the line or curve. Curves are a bit tricky for developing accurate equations, as one must start by assuming the appropriate type of curve (circle, parabola, quartic, exponential, etc. - it's a LONG list) and then determine appropriate coefficients. And, due to measurement error, there may be a number of curves which all give similarly close fits to the data. For this reason, we often linearise the data - for example, plotting y versus x^2 instead of x will give a straight line if the original relationship would have produced a parabola.
There are techniques to take the guesswork out of curve fitting, which can be found in appropriate mathematical texts.
http://www.mathsteacher.com.au/year10/ch16_statistics/09_linebestfit/24line.htm
https://en.wikipedia.org/wiki/Curve_fitting
You can practice drawing a line of best fit here.
http://illuminations.nctm.org/ActivityDetail.aspx?ID=146
