ArcObjects is a development environment for ArcGIS applications by ESRI.
Overview
ArcObjects is a set of COM-based APIs from ESRI Inc. that are used in several of their products, ArcGIS Desktop, ArcGIS Engine and ArcGIS Server.
The APIs can be used several developer platforms including .Net (VB.Net/C#...), Java, C++.
Tag usage
For non-development questions, see GIS Stack Exchange