What does parameter of interest mean in statistics?
It means just that.
The statistician’s parameter of interest is whatever they were seeking and estimating, the central situation, on which they want to focus their analysis.
An example might be a study investigating the correlation between abdominal circumference and lung function, with their central data point being abdominal circumference as an explanatory variable for lung function. They would then examine how varying other parameters (e.g., pressure) impacted this correlation–not because they care about those other variates so much (although that could also happen), but because in order to make any generalizations complete enough to be helpful or informative, you need to determine what the effects are on your parameter of interest when you change something else within your systems.