The term 0-day refers to those software vulnerabilities that are discovered the very same day the exploit is released (an exploit is a software designed specifically for a scope), which can exploit -no pun!- them for operations that are usually not allowed, and most times of an illegal nature. This term gets its name by the fact that the developer of the system has zero days to patch the vulnerability.

The good aspect of 0-day vulnerabilites is that once they are identified and fixed, they lose any effectiveness, thus securing the affected system.