Let $X_1,...,X_n$ be a random sample from a distribution with mass/density function $f_X$ that depends on a (possible vector) parameter $\theta$. Then $f_{X_1}(x_1) = f_X(x_1;\theta)$ so that
$f_{X_1,...,X_k}(x_1,...,x_k) = \prod_{i=1}^kf_X(x_i;\theta).$
Could someone please explain what the significance of $\theta$ is in the above definition. I've never seen this before. Is it the mass/density function that depends on the parameter or is it the random sample that depends on the parameter.