Classifications were added to Architectural Desktop with the 2004 release, primarily because of a need on the Building Systems side to allow MV Parts to be further categorized into specific types. But they have very relevant and powerful applications in Architectural Desktop as well.
Many times "stock" ADT objects are used to represent something else. For example, a wall style might be used to represent a countertop or base cabinet (in fact, this is the case with the "stock" content in the Design Tools catalog). A slab might also be used to represent a countertop. But for display and scheduling purposes, ADT still "sees" these objects for what they really are - walls and slabs.
When it comes to scheduling, you can tell a schedule to ignore things on certain layers, but how do you tell a display configuration that something isn't really a wall - but is something totally different. For that matter - find a display representation for "Cabinetry". (Don't bother - there aren't any). And, wouldn't it be nice if, in the case of the schedule, you didn't have to remember to filter out certain layers, but instead a property of the schedule style itself could tell it to ignore walls that really aren't walls? This is all possible with classifications.
All a classification style definition consists of is a list of, well, classifications that you can assign to object styles. Because they're nothing more than a list, they are extremely easy to create. Even better, there is already a perfectly functional, and in my opinion, adequately complete, classification style defined for you. In the "Styles" folder of your Content directory (follow the "Content" shortcut in your ADT file dialog), there is a drawing file that contains the Uniformat II Classification Definition (look at the file names - it will be obvious). I would recommend importing this classification directly into your standard ADT template. Or you can create your own, based on some other standard, such as MasterSpec. Try the Uniformat II version first, however - I suspect you'll find it more than sufficient for your needs. If you DO decide to "roll your own", make sure you check on ALL object types in the "Applies to" tab. That way you can attach it to any object style that you create.
Assuming you're using the Uniformat II definition however, here are a couple of examples of how you can apply it:
1) A wall that is not a wall: You may have customized your "Reflected" display configuration to show objects below the cut plane for walls, so that you can see the wall opening lines. However when you do this, you'll notice that suddenly toilet partitions and countertops created with the plumbing layouts in the "Design" catalogs are showing. You probably don't want those on your reflected ceiling plans, but since they're walls, the display system shows them. You have a couple of options, admittedly, in addition to using classifications. First you could just freeze their layer. Second, you could edit the "wall" styles that represent these objects and place a style-level display override on their "Reflected" display representation. Or, you can simply edit their style, and on the "Classifications" tab, assign them the "Plumbing Fixture" classification that will already be available from the "Uniformat II" listing (assuming you've already imported the classification definition into your drawing). Now, in your Reflected Display Set, go to the "Display Options" tab - you'll see all of the Uniformat II classifications listed. Simply select "Plumbing Fixtures" and change the setting from "Show" to "Hide". Now, even though you are instructing walls to display, any "wall" that is classified as a plumbing fixture will hide!
(Note: the goal, of course is to automate this. To do so, edit the wall styles in the original files that contain the plumbing layouts, and make the display setting in your ADT template).
2) Scheduling Door/Window Assemblies as mulled units in a door schedule: When you use a door style as an infill definition in your assembly style, do NOT classify it as anything. This means of course, that door styles used in assemblies should be unique and separate from doors that stand alone. Door styles that are by themselves (not part of an assembly definition), should be classified as either "Exterior Door" or "Interior Door". The assembly itself, that contains a door style as an infill definition is also classified as either an "Exterior Door" or "Interior Door". Next, redefine your door schedule. Under the "Applies to" tab, if you have the classification definition loaded in your drawing, you can instruct the schedule style to apply to not just "Doors" and "Door/Window Assemblies", but further only to apply to those that are classified as "Exterior Doors" or "Interior Doors". This, by the way, will also prevent those toilet partition doors from appearing in your schedule. You need to also make this change to the property set definitions that are driving the schedule, so that you don't accidentally tag doors that aren't really doors. Again, to automate this, these settings should be made in the original content files - the original door schedule and property set definitions.
The main thing to remember after you've modified your schedule, property set definitions and display sets, is to make it a part of your regular style definition process to classify EVERYTHING. You never know when you'll need to use that classification!