The practical meaning of Prior Distribution

The prior distribution of a parameter θ must be a probability distribution over the parameter space. We assume that the experimenter or statistician will be able to summarize his previous information and knowledge about where in  the value of θ is likely to lie by constructing a probability distribution on the set . In other words, before the experimental data have been collected or observed, the experimenter’s past experience and knowledge will lead him to believe that θ is more likely to lie in certain regions of � than in others. We shall assume that the relative likelihoods of the different regions can be expressed in terms of a probability distribution on , namely, the prior distribution of θ.

Prior Distribution doesn't matter

It is very often the case that different prior distributions do not make much difference after the data have been observed. This is especially true if there are a lot of data or if the prior distributions being compared are very spread out.

a posterior distribution is calculated after a prior distribution is specified.

The above relation (7.2.10) states that the posterior p.d.f. of θ is proportional to the product of the likelihood function and the prior p.d.f. of θ.