Use the Offset Path when you want to make a larger or smaller replica of your object.

Why not use the Scale Tool? Take a look:

Here's the Object:

Double-click on the Scale Tool (S) in the Tools Panel to open the Scale Tool dialog box (see images below):

To make in inner outline - Scale was then set to 50% (and Copy was clicked) - and this was the result :

NOTE: If your Object was filled with color and you wanted just an outline - click D for Default Fill and Stroke (which is a white Fill and a 1 point black Stroke).

As you can see - the scaled-down image is not quite right.

So, instead, select your Object and then go to
Object - Path - Offset Path to open the Offset Path dialog box (see image below):

The default Offset is 10 pt and after clicking Preview, this is the result (see image below):

After setting the Offset to -7 (negative seven) for an inner outline - this is the result (see image below):

If the Joins edges needed to be sharper - the Miter limit could be increased. Round and Bevel are also available as choices for Joins (see images below):

Below, Round was chosen for Joins:

Any questions?

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