A customer is hurt at your place of business and sues.
A judgment against the business is generally paid from business assets. Your house and personal savings are usually out of reach, provided the company has been run as a separate entity.
General liability insurance typically pays a covered claim and the cost of defending it, up to the policy limit, so the business is not paying out of its own accounts.
The LLC protects you; the policy protects the business. Without the policy, the business itself can still be emptied by one claim.