The QBO format is the format to import transactions into QuickBooks. ".QBO" does not mean "QuickBooks online".
QuickBooks Desktop has to be not older than three years to import .QBO files. For example, if the current year is 2017, QuickBooks 2015 is the oldest desktop version that can import QBO files.
IIF format is the format to use for older QuickBooks versions. Look for converters converting to the QBO format.
QuickBooks Desktop (PC or Mac) imports QBO files through File-Utilities-Import-Web Connect format.
QuickBooks Online imports QBO files as well and the QBO format is the best format it imports. QuickBooks online also imports OFX and QFX files (also good choice to import). OFX and QFX formats are not importable by QuickBooks desktop.
QuickBooks desktop imports QBO (Web Connect) files into the Bank Feeds center. Once the transactions are imported, you review them and match to vendor records and assign expense/income account. After that, the transactions are added to the register.