ECAD stands for electronic computer-aided design. Libraries are containers to store components in. Components may consist of schematic symbols, PCB footprints (shapes), simulation models and a lot of other parameters, like MPN (Manufacturer Part Number), manufacturer, value, etc.
Components Library Management is to ensure every team has access to the correct component information on-demand. This helps designers to stay productive and focus on designing great new products, Components engineers to handle the up-to date list with revision history of components and Procurement team to maintain the sourcing of components based on the stock availability.