Transaction Assist shows you the visit history leading up to a transaction and allows you to create and analyze your own marketing attribution model. Visitors interact with your site across multiple visits and multiple sources, but web analytics will typically only give credit for a conversion to the last touch or visit. Ad conversion tracking, such as Adwords or Shopping Comparison Engines, will give credit to the first touch. These different methods of attributing credit will in turn give you different reports that are hard to reconcile.
The example above shows the visit history leading up to a transaction. The first touch came from an Adwords ad, but the last one was from Google Organic. Adwords reporting will show a conversion, but web analytics will credit the conversion to the last Google Organic visit, not the initial Adwords visit. You can also see interactions in between that have provided valuable assists that may have played an important role in the conversion process, but which would be hidden in web analytics reporting.