From my understanding, the Precise Structure column is used to identify which sub-assemblies and/or components are out of sync with the Precise BOM in Teamcenter:
Per the NX10 docs:
The Precise Structure column in the Assembly Navigator shows the subassemblies and parts in NX that are no longer the same as those in Teamcenter. This applies when the saved precise assembly in Teamcenter Structure Manager differs from the current loaded precise assembly in NX.
When you open an assembly in NX, then modify the assembly in Teamcenter Structure Manager such as by revising a component, and save the assembly, the assembly in Teamcenter is no longer the same as the assembly in NX. To see the components in NX that differ, right-click in the Assembly Navigator and choose Refresh Teamcenter Information . The Precise Structure column identifies the components that are modified.