This code inspection checks violations of your preferences for using var or explicit type in local variable declarations. Specifically, it checks variable declarations of C# built-in types (bool, double, string, etc.).
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For variable declarations of other types, ReSharper provides similar code inspections, which you can configure separately.
Using implicitly typed local variables (also known as var keyword) introduced in C# 3.0 has become quite popular as it improves readability in many scenarios. By default, ReSharper also encourages using of var keyword, but preferences of its usage are flexibly configurable — for example, you can opt for using explicit types in specific cases or everywhere and ReSharper will help you enforce your preferences.