Technically, if your employer asks you to resign, it is indeed a sort of negotiation. If they can't afford to fire you, and you miss out on a severance package if you resign yourself, then you might want to be compensated in some way, and you might be able to negotiate with your employer.

What does it mean to be asked to resign?

When you're forced to resign, you're going to have to leave your job at some point, but you may be able to negotiate your separation from the company. As the company no longer wishes to continue your employment, you may have an advantage in the negotiations—unless you are about to be terminated for cause.

Is being asked to resign the same as being fired?

Resignation means the employee has decided to sever the employment. We usually call this quitting. Termination means the employer has decided to sever the employment. We call this being fired, terminated or laid off.