Bill of Materials (BOM) synchronization is the process that considers the differences in product structure and BOM Line properties. Having BOM Sync turned on indicates you are making changes outside the Solid Edge environment, typically in a Teamcenter PDM client or Structure Editor, then expecting to see the changes in Solid Edge.
BOM synchronization is controlled by the Teamcenter preference SEEC_BOM_Synchronization. It is delivered by the Solid Edge Embedded Client administrator and is set to FALSE (off) by default.