Check out this short paper on “Variables and parameters” by Douglas Altman and J. Martin Bland, who identify at least three different meanings of the statistical term “parameter” and attempt to distinguish parameters from variables as follows (note: the introductory labels in bold are mine):
- Parameters as statistical quantities: “… parameters [unlike variables] do not relate to actual measurements or attributes but to quantities defining a theoretical model,” such as the mean and standard deviation of the data pictured in the figure pictured below.
- Parameters as slope-intercepts: “Another use of the word parameter relates to its original mathematical meaning as the value(s) defining one of a family of curves,” i.e. the slope and intercept of a line or curve.
- Parameters as variables(!): “In some contexts parameters are values that can be altered to see what happens to the performance of some system.” (Wait, isn’t this what a “variable” is?)
So, which is it? In the alternative, is the definition of the term parameter provided by Wikipedia (see here) even less helpful?
prior probability 
I always thought of parameters as something like coefficients, i.e., the model sense — but having more “meaning” than a simple coefficient — something along the line of dimensionless constants, for example.