What is an OODB?

An OODB is a database where the natural unit of storage is an object. Just as fixed length rows in tables are the natural unit of storage in a RDB, objects are the natural unit of storage in an OODB.

There are several advantages of an OODB when working in an OO language like C++:

There is no need to do "data modeling" as the unit of storage is the object.
There is usually no need to translate between the language's type system and the database's type system as they are the same.
There is no need to translate objects into rows and rows into objects, as there is when using a RDB. For certain types of applications, this means that the runtime performance of an OODB can be superior to a RDB.
OODBs use implicit persistence. This means that the user of the OODB does not have to worry about loading and saving his objects; about when they are in memory and when they are only on the OODB. This is all done transparently by the OODB.

These advantages are especially important in applications where the data consists of a small number of objects that have complex interrelationships, and you won't be making many queries. RDBs tend to perform better when you have a large numbers of objects with simpler interrelationships and where you'll be creating boatloads of queries.