The geographic coordinate systems warning appears whenever data you are adding uses a different geographic coordinate system than the one used in the map or globe you are adding it into. Why is this information important? ArcMap and ArcGlobe can convert data between coordinate systems. This is often called projecting the data. If the source and target coordinate system do not use the same geographic coordinate system, data can be shifted anywhere from a few meters to hundreds of meters from the correct locations.
The table lists any data sources that you are adding and their geographic coordinate systems. The coordinate system of the data or the map/globe may be a projected coordinate system like Universal Transverse Mercator (UTM). Each projected coordinate system is based on a geographic one. The dialog box retrieves the geographic coordinate system information from the data sources and the map or globe.
Converting correctly between two geographic coordinate systems requires a geographic, or datum, transformation. ArcMap doesn't automatically choose a transformation for you, because there are often multiple transformations that could be applied between two geographic coordinate systems. Transformations can differ by method and parameters that affect their accuracy, or by area of use. It is up to you to decide which transformation is most appropriate for your data and your purposes.
The Transformations button will open the Geographic Coordinate Systems Transformations dialog box, where you can see what already defined transformations are available or define a custom or compound transformation. The transformations in the drop-down list are ordered with the best option first. Or, if you prefer, you can access the Geographic Coordinate Systems Transformations dialog box via the data frame's Coordinate Systems tab.
This Geographic Coordinate Systems Warning dialog box will not appear if you add data later that does not have the map or globe's coordinate system if you have set a geographic transformation. If the transformation is between the same coordinate systems, it will treat the set one as the default.