A graph explorer is a tool that lets you inspect data stored in a graph database.
This can range in complexity from a simple query-answer system that returns the data you request, to a visualization of the whole graph that displays data in a human readable way, allowing you to navigate your database in business-friendly, easy-to-understand way. The RDFox console is an example of both.
Graph explorers allow the user to gain a better feel their data to aid in understanding it, or to help them spot errors. They can also be used to assist in validating data models as they are developed or queries as they are written and rewritten, as mistakes are easier to spot when visualized.