You can look up the the exact wording of the working-space rule in Section 110.26 of the electrical code. While you can't download any part of the standard without payment, you can read it here free, legitimately provided you fill out the National Fire Protection Association's registration. NFPA encourages you to buy copies or interactive online access. If you don't need those, you can ignore the marketing.

How serious is this?

Even if you want wiring elsewhere in your house examined, clear access to your panel is needed.

If, say, a plumber has installed equipment in that space, they violated the electrical code, breaking the law, however unwittingly—and if you hired them, you're considered responsible! An electrician is not professionally qualified to relocate plumbing equipment, or ducts, or doors or walls; all of these have been in the way, one time or another. Consequently, wiring in such a space will be examined only in an emergency, and only long enough to avert a crisis.

What makes this so important?

An electrician should kill power at its source whenever possible. People are fooled, and suffer shock or worse, every week because they assumed they could shut off power by just flipping a switch, or because they figured they could get away with working on energized (a.k.a live) wiring.

A common wiring design known as the multiwire circuit can endanger even someone who has reason to believe they have killed power. By looking inside the panel and identifying how wiring enters it, a professional should be able to identify and deenergize (shut off power to) such circuits. This protection can go out the window if anyone working downstream, meaning after the wires left the panel to feed outlets, mixed up the circuits they spliced. Nonetheless, identifying the wiring inside the panel is a sensible professional's first step.

This clear space also enables you to shut off power fast when something goes wrong.