From the reference I give below: $R^2$ is explained as,
$R^2$ = $Explained \ Variation / Total \ Variation$
1) $R^2$ is always between 0 and 100%:
2) 0% indicates that the model explains none of the variability of the response data around its mean.
3) 100% indicates that the model explains all the variability of the response data around its mean. the "variation divided by the total variation."
Also from another reference:"...The coefficient of determination, $R^2$, is useful because it gives the proportion of the variance (fluctuation) of one variable that is predictable from the other variable. It is a measure that allows us to determine how certain one can be in making predictions from a certain model/graph." In http://mathbits.com/MathBits/TISection/Statistics2/correlation.htm
Since expansion and contraction was covered by the other answer, I just want to make some comments on of aspects that effect the $R^2$. An important part of $R^2$, is the selection of the function used to fit data. You could have functions that would have have the same expansion or contraction and they can have different $R^2$. With the results you mention and the $R^2$ given I would be incline to try a polynomial (in you independent variable) to see how it fits. This function that contains multiple terms that are powers of x that would fit best, which would mean you can try a polynomial fit. In the most general case of the polynomial, you would use spline regression to find an fit. The $R^2$ review is the first step in analyzing data. Note: "Pearson Product-Moment Correlation" (which can be found on the Internet) discusses using $R^2$ to determine the "strength of the correlation."
The general reference on regression (and also "over fitting") I mention above a few times on how to interpret the correlation coefficient is "Regression Analysis: How Do I Interpret R-squared and Assess the Goodness-of-Fit?" is
Lastly, just want to make a general comment on function selection vs model. A model is development from the principles and laws of the field of study you are working in. In many case a model is developed even before data is collected (e.g. Theoretical Physics -- I have done this many times). On the other hand just selecting functions to try to "fit" data from experiments is not classified as a model. You are just looking for the best fit to the data (again as a first step) -- then others could study your data and develop/derive a model.