What's the difference between accessing data with dataset or data reader?

The dataset is generally used when you like to employ the disconnected architecture of the ADO.Net. It reads the data into the local memory buffer and perform the data operations (update, insert, delete) locally to this buffer.
The data reader, on the other hand, is directly connected to the database management system. It passes all the queries to the database management system, which executes them and returns the result back to the application.
Since no memory buffer is maintained by the data reader, it takes up fewer resources and performs more efficiently with small number of data operations. The dataset, on the other hand is more efficient when large number of updates are to be made to the database. All the updates are done in the local memory and are updated to the database in a batch. Since database connection remains open for the short time, the database management system does not get flooded with the incoming requests.