With ArcGIS 9.1 and earlier versions, geoprocessing tools produced 32-bit data. The output of geoprocessing tools in ArcGIS 9.2 and later versions is 53-bit. This message informs the user of the higher resolution of the output data from the geoprocessing operation.
The term 'larger resolution' used in the context of this message means 'higher resolution'. The message does NOT mean that the resolution of the data is lower than in previous versions, or in different data formats.
Higher resolution means that the precision of the data is INCREASED.
This does NOT mean that the data has been made more accurate. The accuracy of the data is determined when the data is collected.
See the link in the Related Information section below for a description of the new high-precision data storage available in ArcGIS Desktop at version 9.2 and later versions.
Wikipedia provides an excellent discussion of the concept of accuracy versus precision at the link below.