One of the most common definitions of metadata is that it is information about information. But the information that it describe varies. It could be a document, spreadsheet, audio or image. Metadata could also provide a description about application workings. The definition could then further be defined according to how metadata is applied.
In the case of geospatial metadata, metadata works to describe geographic objects such as maps, datasets and anything else that has any geospatial components. The Geographic Information System or the GIS is there to provide software and data for geographic places information management and retrieval, for analysis of spatial relationships and also for model spatial processes. GIS also offers a framework for collecting and organizing spatial information and other related data so that such information can be shared, viewed and analyzed.
ArcGIS, on the other hand, refers to a group of commercially available GIS products. There are standards for creating ArcGIS metadata. The Federal Geographic Data Committee has Content Standard for Digital Geospatial Metadata, which aims to give a comprehensive description for every data source.
Of course, following the standard has its advantage. The availability of tools for the creation and validation of the metadata is one. Following the standard will facilitate data sharing with a wider audience since having the same standard means following the same vocabulary and terminology. Data would easily be understood across different organizations, across different agencies and even across different countries. Collaboration and other researches will be aided with the data they get from various other sources.