To Network means to meet or come in contact with other people to share information, contacts or other help or to communicate with and within a group. In the first example, Tim is using Facebook to network for a job. In the second example, Kitty is networking with all her friends on Facebook for a volunteer group that helps the homeless.
This idiom can be found in the LSI textbook Speaking Transitions. This book is used at LSI schools in the level 4 Listening/Speaking classes. For more information, please visit: www.languagesystems.com