The schema defines classes of NDS objects (such as Users, Printers and Groups) and which information is required or optional at the time that NDS object is created. Every NDS object has a schema class that has been defined for that type of object.
The base schema is the schema that ships with NDS. The difference between the base schema and the extended schema is simple. Once the base schema has been modified in any way---such as adding a new class or a new attribute---then it is considered the extended schema.
You don't need to extend the schema, but you have the ability to do so. The Schema Manager tool in ConsoleOne allows the schema to be extended as needed to meet organizational needs. For example, you can extend your schema if your organization requires special footwear for employees and you need to keep track of employee shoe sizes. You can create a new attribute called Shoe Size and then add it to the User class.