Under COBRA, eligible individuals are able to continue their group health insurance benefits through their employers. The reason COBRA seems so expensive is because the former employee is now responsible for 100% of the premium and potentially an additional 2% administrative fee. The sticker shock is because many employers subsidize a percentage of the health insurance premium for their workers.
On average, employers subsidize ~70% of the health insurance costs for their full-time employees. However, post-employment the employer subsidies typically end, and if the individual continues on their former employer's group health plan they are now responsible for the full cost of the insurance. It's not uncommon to see a 300-500% increase in their monthly premium for the same exact coverage when an individual elects COBRA.