What is hierarchical prior in Bayesian statistics? What are hierarchical priors? 
How do they differ from the general concept of priors?
 A: When you have a hierarchical Bayesian model (also called multilevel model), you get priors for the priors and they are called hierarchical priors. 
Consider for example:
$z = \beta_0+\beta_1{y}+\epsilon, \\ 
\epsilon \mathtt{\sim} N(0,σ)\\ 
\beta_0\mathtt{\sim} N(\alpha_0,σ_0),
\beta_1\mathtt{\sim} N(\alpha_1,σ_1),
\beta_2\mathtt{\sim} N(\alpha_2,σ_2)\\

\alpha_0\mathtt{\sim} inverse-\gamma(\alpha_{01},\theta_0)\\
$ 
In this case, you can say that, $inverse$-$\gamma$ is a hyperprior. 
EDIT:
This was very useful to me when I learned about Hierarchical Bayesian Modeling.  For an in depth explanation  and detail, you may refer to Gelman's Data Analysis Using Regression and Multilevel/Hierarchical Models. 
A: A regular Bayesian model has the form $p(\theta |y) \propto p(\theta)p(y|\theta)$. Essentially the posterior is proportional to the product of the likelihood and the prior. Hierarchical models put priors on the prior (called a hyperprior) $p(\theta |y) \propto p(y|\theta)p(\theta |\lambda)p(\lambda)$. We can do this as often as we want. 
See Gelman's "Bayesian Data Analysis" for a good explanation.
