ArcGIS Desktop is software that allows you to discover patterns, relationships, and trends in your data that are not readily apparent in databases, spreadsheets, or statistical packages.

Beyond showing you your data as points on a map, ArcGIS Desktop gives you the power to manage and integrate your data, perform advanced analysis, model and automate operational processes, and display your results on professional-quality maps.

ArcView
ArcView is geographic information system (GIS) software for visualizing, managing, creating, and analyzing geographic data. Using ArcView, you can understand the geographic context of your data, allowing you to see relationships and identify patterns in new ways.

With ArcView, you can

• Author maps and interact with your data by generating reports and charts and printing and embedding your maps in other documents and applications.
• Save time using map templates to create consistent style in your maps.
• Build process models, scripts, and workflows to visualize and analyze your data.
• Read, import, and manage more than 70 different data types and formats including demographics, facilities, CAD drawings, imagery, Web services, multimedia, and metadata.
• Communicate more efficiently by printing, publishing, and sharing your GIS data and dynamic content with others.
• Use tools such as Find, Identify, Measure, and Hyperlink to discover information not available when working with static paper maps.
• Make better decisions and solve problems faster.

ArcEditor
ArcEditor is a powerful GIS desktop system for editing and managing geographic data. It includes all the functionality of ArcView along with additional advanced editing tools to ensure the quality of your data. ArcEditor supports single-user and multiuser editing, allowing you to disconnect from the database and edit in the field.

With ArcEditor, you can

• Allow multiple users to simultaneously modify and edit data.
• Build and maintain spatial relationships between features using topology rules and a process called validation.
• Support multiple workflows, manage work order processing, and implement QA procedures for validating edits.
• Monitor the database over time and evaluate what-if scenarios.
• Perform raster-to-vector conversion and create data from scanned maps.

ArcInfo
ArcInfo is the most complete desktop GIS. It includes all the functionality of ArcEditor and ArcView and adds advanced spatial analysis, extensive data manipulation, and high-end cartography tools. Organizations use the power of ArcInfo every day to create, edit, and analyze their data in order to make better decisions, faster. ArcInfo is the de facto standard for GIS.

With ArcInfo, you can

• Perform advanced GIS data analysis and modeling.
• Take advantage of tools designed for overlay analysis, proximity analysis, surface analysis, and raster processing and conversion.
• Publish and convert data in many formats.
• Create and manage personal geodatabases, multiuser geodatabases, and feature datasets.
• Use high-end cartography tools to generate professional-quality, publication-ready maps.
• Design customized symbols and place sophisticated annotation and labels on your maps.

ArcReader
ArcReader is a free, easy-to-use desktop mapping application that allows users to view, explore, and print maps and globes. Anyone with ArcReader can view high-quality interactive maps authored by a higher-level ArcGIS Desktop product and published with the ArcGIS Publisher extension.

With ArcReader, you can

• View, navigate, and print published ArcGIS maps using ArcReader (.pmf files).
• Deploy your GIS data to novices and professionals alike.
• Zoom, pan, and switch between map and page layout view.
• Communicate more efficiently with the ability to graphically mark up maps.
• Print published map and globe documents including all layer symbology and cartographic map elements on any supported printer.
• Create custom ArcReader applications and embed ArcReader capabilities into existing applications.

Extensions for ArcInfo, ArcEditor, and ArcView

Using optional extensions with ArcGIS desktop products allows you to perform extended tasks such as raster geoprocessing and three-dimensional analysis. Unless noted, extensions can be used with ArcInfo, ArcEditor, and ArcView.

More information here