Once you're out on the track, the only means track officials will have to communicate with you is via flags. So it's extremely important for you to know who will wave the flags (corner workers, and start/finish line), and what they mean. Below is a description of the meaning of all the common flags. Note that these definitions are common in the USA, and where ARC/NCRC run. You may find slight changes under FIA rules.

Command Flags

The first set of flags are "command flags", in the sense that you MUST do something based on seeing them.

RED FLAG
This flag means a major incident has happened, that will require an emergency vehicle on the track. Stop your car in a safe way, within view of a flag station, as soon as possible. Stay on the track, but pull off-line so emergency vehicles can get by.
BLACK FLAG
An open waiving black flag by any or all corner workers means that there has been an incident on the track that necessitates bringing all cars to the pits. It's likely a car is stranded in an unsafe area requiring a tow truck. If when you are passing the main tower or other designated flag station, and see the black flag waving at you then it's typically due to an unsafe action on your part, and you must pull into the pits to have a discussion with the track steward. It is also possible that a furled black flag may be pointed at you if you are driving in a group of cars (pointed to differentiate you from others), you are to also pit under this circumstance.  Waving, furled/pointed black flags are taken very seriously, too many instances will cause you to be removed from the event.
MECHANICAL FLAG This flag (also referred to as the "meatball flag") means that the turn workers have noticed a mechanical problem with your car (fluid leaks, loose car parts, sound violation at certain venues, etc). Proceed to the hot pits, and talk to the Steward at the start/finish, and likely then proceed to the paddock and correct what is wrong.
CHECKERED FLAG You'll see this flag at the start/finish line, and possibly at an earlier station as well. It means the session is over. Complete the lap at a "cool down" pace, and exit into the paddock area. Be aware that passing is still allowed on the checkered flag lap.

Information Flags

This second set of flags are "informational" in the sense that while a track official is telling you something, and it may be prudent to take action, you're not fundamentally required to do anything. Please note that while the Caution and Passing flags are correctly listed as Informational, at an NCRC event you absolutely must respond correctly to them and will be black-flagged if you do not.

GREEN FLAG This flag is waved at the start of a session or race, or any time you're past an incident. It can be waived after a local or full track yellow, for example.
YELLOW FLAG This flag notes caution. The flag can be displayed by all corners and the starter ("full course caution") or only a corner or two ("local caution"). Some tracks will use double waiving flags to represent full course caution. In either case, within the range of yellow flags you should slow down and be prepared to find a car spun on or off the track. There is no passing allowed in a caution zone. Once free of the caution, the following corner may display a green flag to signify that normal driving is acceptable or more likely the next flag station will not be displaying any flag in which case normal driving is also acceptable. 
PASSING FLAG This flag is displayed at a specific car, and is an encouragement to note mirrors, there are cars in passing position. At NCRC Open Track events, this should be taken as a mandatory requirement to point the following driver by and allow the pass - you have cars behind you and must let them pass in the next passing zone or you will receive a black flag. In an ARC race, a blue flag is always informational.

At non NCRC events, the passing flag is normally an informational flag.
SURFACE FLAG This  flag is also called a Debris Flag, and indicates there is something on the surface of the track that may make it unsafe. It could be oil, rain, gravel, etc. It can be "local" or "full track", the same way as a yellow flag, and it's advisable to slow a bit for the relevant portion of the track. Once you've been by the debris zone (seen a corner not waving the surface flag), you're welcome to drive full speed if it makes sense, including going through the zone at full speed on the next lap.
WHITE FLAG This flag is not always used, but will signal one lap before the checkered flag. It can also mean that there's a slow vehicle on the track. At ARC & NCRC events we do not use this flag. During a race, the halfway point is signaled by crossed green and white flags, and the final lap is signified by one finger in the air from the starter.