When a technical person (developer, engineer, scientist, et al.) uses a UI tool to solve a problem instead of the command line or underlying program.
The 'elephant' comes from the PostgreSQL elephant and the many related SQL GUI clients that allow developers to avoid using SQL from the command line for queries. However, this phrase is not limited to PostgreSQL and can refer to any other GUI or related to tool that allows a user to click around to find their way.
This phrase originated at Even Financial, an incomparable Fintech company in the heart of NYC.
Alex: I use the debugger to step-through my code when there's unexpected behavior.
Ross: STOP ELEPHANT CLICKING, YOU ELEPHANT CLICKER!!!