Adobe A4T is and abbreviation for Adobe Analytics for Target. It is an integration between Adobe Analytics and Adobe Target. I prefer to use Analytics for reporting all of my Target tests and activities. There are a couple of benefits to using Adobe A4T.
1. Reporting. Target's reporting is good, but using Analytics for reporting is better because you get all of the benefits of analytics reporting. This includes segmentation, audiences, conversion metrics and the customization you can build into a Analytics report. You can get much more detailed and customized in Analytics than you can analyzing a test in Target alone.
2. Single Source of Data. If you are already using Analytics, its nice to have everything in one place. Rather that two separate data source, you can do all of your reporting in Analytics. Its much cleaner.
3. Audience Segments and Conversion metrics. You can create audiences, segments and conversion metrics in Analytics and then use them in Target. This includes calculated metrics. Similar to a single source of data, this makes it so you can do traffic and test analysis on the exact same segments and audiences. It also means you don't have to maintain or try to duplicate audiences in two separate systems.
4. Post Test Analysis is better. With reporting in Target, you have to set up all of your segments that you want to analyze and all of your success metrics before you run the test. Not true with A4T. With Analytics as the reporting source, you can add new segments and conversion metrics after you have run the test. This allows for deeper analysis of the test without and gives you greater flexibility so you aren't locked into only the segments and metrics that you thought of before you ran the test.
Overall, the experience of using Adobe A4T is much better than Target alone. Once you implement it, you'll find you'll set up a test in Target and then do all of your analysis in Analytics. Its great.
Here's a link for implementation.
https://docs.adobe.com/content/help/en/target/using/integrate/a4t/reporting.html