QBO format is the format to import transactions into Quickbooks (.QBO is not "Quickbooks online").
Quickbooks Desktop has to be not older than three years to import .QBO files. For example, for current 2016 year, Quickbooks 2014 is the older Quickbooks desktop version that can import QBO files.
For older Quickbooks versions, please use IIF format or converters that convert to IIF format.
Quickbooks Desktop (PC or Mac) imports QBO files through File->Utilities->Import->Web Connect format
Quickbooks Online imports QBO files as well and 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.