Circuit (Network) analysis is the process of finding the voltages across, and the currents through, every component in the network. Consider using in conjunction with tags for the particular analysis technique(s) in question: "nodal-analysis", "mesh-analysis", "superposition", "transients" ,"steady-state-analysis" etc.
A network, in the context of electronics, is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, every component in the network. There are many different techniques for calculating these values. These techniques generally assume that the components of the network are all linear.
See Wikipedia's article on network analysis for more information.