Microsoft wanted to make Cortana as much like a real personal assistant as possible, and to that end included a notebook in the platform. Cortana's notebook includes all the pertinent information she's learned about you through how you use your phone. Users, however, have control over the notebook, and can edit it as they choose.
Cortana also replaces the search function on Windows phones. When you activate Cortana, you can either complete your queries by voice or through typing.