A secure connection allows your web browser to use its 128-bit encryption features. This means the communications between you and your iDM account will be unreadable by anyone 'listening on the line'. The trade-off is reduced speed for transfering files, as each piece of data is encoded and decoded throughout the process.
You may want to enable a secure connection when transfering sensitive data such as payroll documents, and disable it when transfering data such as photos from the family vacation.