There are two types of EXTRUDE that can be used in Cubify Invent. They are EXTRUDE (Boss) and EXTRUDE (Cut).
Essentially, EXTRUDE (Boss) ADDS layers of material in the shape of the 2D sketch to form a 3D object with features defined by the 2D sketch. I don't think that it's a stretch to call EXTRUDE (Boss) the most used 2D to 3D option.
Using EXTRUDE (Boss), a 2D circle becomes a 3D Cylinder having height as well as a circumference. A 2D square becomes a 3D box or cube when EXTRUDE (Boss) is applied.
EXTRUDE (Cut) doesn't ADD material. It REMOVES material, if any exists. This is most often used to create cut-outs and holes in already existing 3D objects. While not used as often as its boss counterpart, it is still an often used option and may well be second of all the 3D options in frequency of use.
Using the selected 2D sketch, it acts as a cutting die, removing the exact shape of the original 2D sketch from whatever 3D object is crosses. It can cut partially through an object or all the way through as the user determines.
Here is a video that demonstrates these powerful Cubify Invent commands at work creating a useful part that has bolt holes and a ledge that is counter-sunk into the part using EXTRUDE (Cut).
For those exploring Moment of Inspiration, here is how a similar part might be created using only EXTRUDE (boss) with MOI's Boolean Union and Difference Tools. It's interesting how different applications accomplish the same task by going down two different paths.
In a follow-up tutorial, we explore all the 2D and 3D BOOLEAN FUNCTIONS available in Moment of Inspiration.