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.

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.