The intelligent information society, which is highly digitized, intelligence inspired and globally data driven, will be deployed in the next decade. The next 6G wireless communication networks are the key to achieve this grand blueprint, which is expected to connect everything, provide full dimensional wireless coverage and integrate all functions to support full-vertical applications. Recent research reveals that intelligent reflecting surface (IRS) with wireless environment control capability is a promising technology for 6G networks. Specifically, IRS can intelligently control the wavefront, e.g., the phase, amplitude, frequency, and even polarization by massive tunable elements, thus achieving fine-grained 3-D passive beamforming. In this paper, we first give a blueprint of the next 6G networks including the vision, typical scenarios and key performance indicators (KPIs). Then, we provide an overview of IRS including the new signal model, hardware architecture and competitive advantages in 6G networks. Besides, we discuss the potential application of IRS in the connectivity of 6G networks in detail, including intelligent and controllable wireless environment, ubiquitous connectivity, deep connectivity and holographic connectivity. At last, we summarize the challenges of IRS application and deployment in 6G networks. As a timely review of IRS, our summary will be of interest to both researchers and practitioners engaging in IRS for 6G networks.