Hierarchical Linear Modeling:
Hierarchical linear modeling is an approach to analysis of hierarchical (nested) data  i.e. data represented by categories, subcategories, ..., individual units (e.g. school > classroom > student).
At the first stage, we choose a linear model (level 1 model) and fit it to individual units in each group separately using conventional regression analysis . At the second stage, we consider estimates of the level 1 model parameters as dependent variables which linearly depend on the level 2 independent variables. The level 2 independent variables characterize groups, not individuals. We find level 2 regression parameters by a method of linear regression analysis.
There may be more than 2 levels in this process, provided there are more than two levels in the hierarchy of groups or categories, e.g. district > school > classroom > student.
Technically, hierarchical linear models are such models that for any term all effects of lower order are also included in the model.
For example, for twoway KxN contingency table s, the independence model

and the saturated model

are the only hierarchical linear models that involve both variables.
The following model is an example of a nonhierarchical model:

This model is nonhierarchical since it does not contain the term l_{i}^{X} but contains the higher order effect l_{ij}^{XY} .
If the linear relationship is postulated between the logarithm of the dependent variable(s) and parameters of the model, the models are named "hierarchical loglinear models".