Some tools update their own data on a schedule, even when you haven't opened the app — for example logging the gold price once a day, so the full trend is there next time you look. That's a background task.
Background tasks never send notifications, and their data stays on your devices; with Sync across devices on, it's encrypted and synced to your other devices. When you install a tool, the sheet lists its background tasks and how often they run; installing means you agree. When an update adds background tasks, you're asked first.
If you'd rather it didn't run, turn it off per tool in Me › Background tasks. Anything in that tool that relies on this data stays as it was when you turned it off.
Me › Background tasks also shows when each task last ran and how it went, and lets you run one manually.