Each hospital or clinic can decide how it wishes to manage and inform staff of potential emergencies. "Code White" is a message announced over a hospital’s public address system warning the staff of:
(1) A pending emergency/internal disaster
(2) A paediatric emergency
(3) A violent or combative patient
(4) Severe weather in the area; curtains to be drawn
(5) A power utility outage
Technically, there's no formal definition for a code, but doctors often use the term as slang for a cardiopulmonary arrest happening to a patient in a hospital or clinic, requiring a team of providers (sometimes called a code team) to rush to the specific location and begin immediate resuscitative efforts.
Many institutions use colors (e.g. Code Red, Code Blue) to identify specific types of emergencies. Code Red and Code Blue are both terms that are often used to refer to a cardiopulmonary arrest, but other types of emergencies (for example bomb threats, terrorist activity, child abductions, or mass casualties) may be given code designations, too.
Colors, numbers, or other designations may follow a code announcement to identify the type of emergency that is occurring.
See WebMD's "Code Blue", "Code Black": What Does "Code" Mean? to know more.