Value of Filed Against?
Accepted answer

Do you need to get it programmatically, using server-side Java API?
AbstractService pluginAbstractService = (AbstractService) this;
IRepositoryItemService repositoryItemService = pluginAbstractService.getService(IRepositoryItemService.class);
ICategoryHandle categoryHandle = workItem.getCategory();
ICategory category = (ICategory) repositoryItemService.fetchItem(categoryHandle, IRepositoryItemService.COMPLETE);
String categoryName = category.getName();
2 other answers

These are determined by the Categories specified in the project settings. Open the project configuration in the web client, and then click on the Categories tab. Categories are mapped to teams. Think of it as a way to direct a work item to a team without having to know a specific person on that team (such as when creating a defect). This allows the team to prioritize work items and assign to developers based on their availability.

See https://rsjazz.wordpress.com/2013/01/02/working-with-work-item-attributes/ and the related posts.