Let's first look at bones. Bones objects are like a family, You start with a parent, then have children, grandchildren, etc.. Any bones object can have any number of children but will have only one parent.
There are two ways to manipulate bones objects, directly (there probably is a better word) or inversely.
When You move an object directly, You're moving from a parent's point of view. Any manipulation to You affects all of Your children, grandchildren, etc.. In Imagine You do this by picking in "Pick Group" mode any bones axis and manipulating it. This will also move, rotate, etc.. any bones objects that are down the family tree from it.
When You work inversely (Inverse Kinematics) You are working from the child point of view and affecting all of the way up the family tree. In Imagine You do this by clicking on the "Constrain" menu item.
In direct mode click on the thigh "bone". Rotate it and the shin bone and foot bone move with it.
In inverse or constrain mode click on the foot bone. Rotate it and all of the other bones in the body move. This is because You are affecting up the family tree, and parents always affect down the tree to the other children.
This is where "freeze" comes in.
First click on the hips bone ?:) and click on "freeze" menu item. Check all of the axis in world. This freezes the hips from moving. Now go back, click on "constrain", move the foot bone. The shin bone and thigh bone move with the foot bone but nothing else. You can also use "freeze" to only limit movement to certain axis. In the above example You could keep the shin bone to move only as a knee would bend. Some programs even allow You to limit movement in an axis to a certain number of degrees or range of movement.
As it seems to me, direct mode is useful to pose a figure or object in an unusual pose or where placement is more on looks then on exactness. Inverse mode is useful to position a piece of an object in a certain place.
For example, use direct mode to position a cheerleader's arms. Use inverse mode to place a person's foot up on a step.
Make sure You watch what mode You are in! Direct mode use Pick Group mode and inverse mode uses Pick Object mode.