Is versed the medicine they give you to calm your nerves before surgery?

Yes. Benzodiazepines, such as Versed are the standard pre-anesthesia IV medication that helps calm your nerves.
Versed. Versed, or midazolam, is a hypnotic sedative medication. It is one of the medicines used prior to surgery. It causes you to feel sleepy/drowsy and not remember the surgery. It is not a pain medicine and it does not cause muscles to relax.
Yes. Versed calms nerves prior to surgery, used frequently, & is apparently safe. The beauty of the drug is that it has a retrograde amnesiac effect so patients don't remember much from the preop area as well as moving into the operating room suite.