What is the significance of signing or not signing a delivered written or verbal warning in a work place?

The law does not, as a general matter, require ANY warnings, whether verbal (oral) or written; instead, an employee may be disciplined at will--at any time, for any reason--by the employer, up to and including termination. Warnings are only required if there is an employment contract, a union agreement, or a firm policy of the employer (such as one set out, without limitations, in an employee handbook) requiring them. That said, there are certainly advantages to employers to providing warnings: the chance to improve employee performance and avoid termination; the ability to document the grounds for discipline, to avoid being later accused of improper termination. But while advantageous, they are not required, except as above.