There are two main reasons for developers wanting to configure some features of IntelliJ IDEA to work as they do in Eclipse.
The first reason is when a developer switches to IntelliJ IDEA after years of work with Eclipse they may need some extra time to get fully up and running with the new project structure, keyboard shortcuts and workflows. Finding some familiar settings cuts the downtime to a bare minimum.
The second reason to turn IntelliJ IDEA in Eclipse compatibility mode is when some members of the team use Eclipse while others have switched to IntelliJ IDEA. In this case, the compatibility mode ensures that each member can work at full speed leaving IntelliJ IDEA the burden of keeping projects in sync and both groups of developers happy.
The Eclipse compatibility mode is not a single IDE feature to turn on and off. It results instead from the combination of a few IDE settings: