It's a self contained navigation system that has been around for many years - long before GPS.
The IRS (inertial reference system) is a derative of the INS, which is an acronym for Inertial Navigation System and they work fairly similar. IRS is a newer derative with more advanced functions.
Anyways.
Before the days of fancy FMC's where you typed in waypoint names you'd instead type in their exact co-ordinates like N28'02.8'W016'34.7 in the display unit.
On the Display unit you type in the whole route waypoint after waypoint.
The early models only allowed 9 entries at the time so the crew needed to add additional wpts as the route progressed.
An IRS (modern version of INS, remember) does not only manage the navigation for you,and feeds the aircraft pitch and roll rates, true airspeed, true north, actual wind, groundspeed etc. What sets an INS and IRS apart is: The IRS is able to use the inertial gyros to supply attitude and heading information to the cockpit indicators ( like a flight director or HSI) That's exaclty how it works on glass cockpit aircrafts!
But how does a basic INS work?
One of my books describe's it the best
"If I know where I am now,and if I keep track of each and every movement in all directions from this point on, then I will always know where I am after that"
Easy huh, well in pratice it's not.
This is gonna be a bit hard for me, but I hope you understand.
The INS needs to be aligned before you can start adding waypoints. That is done by telling the INS system where you are, that's why you often see co-ordinates painted on the walls or the ground near a gate. The system is that accurate. You will feed the system different position coordinates if you are at Gate 14 or Gate 15!
It's now the magic begins. INS senses the earths rotation and can after some minutes determine the exact position (this is called alignment)
Okay, why do you need to fill in the start position manually if the INS can tell by itself?
That's just a pre-caution. the INS compare its sensed coordinates with the manually entered and if they agree you have a go!
The INS is so sensitive so it can sense even the slowest moment. Therefore, it is absoulutly forbidden to move the aircraft during alignment. And when you start taxiing the INS senses that you are moving and in turn starts updating the current position continously
The INS is not flawless though, expect some nautical mile error per hour. So after a 14hour flight the INS position may be 20nm (or more) different from the actual true position. These errors can be contained by allowing the INs to peform updates via VOR or DME updating. Nowadays the Inertial system is updated by using the most precise source: the GPS.
The ultimate INS or IRS setup is a triple installation of inertial systems.: Three entirely independent, but interconncted INS's/IRS's. You'll find these tripple installations in every modern airliner.
Nowadays the IRS is not vital navigation wise. GPS is superior so the IRS's role is more to give other information to the aircraft such as vertical speed, azimuth information, pitch and roll rate/angles, winds etc.
If the IRS is not working or not aligned you will have no pitch and roll data, for example. So the fancy PFD and ND will be pretty useless, just take a look at this pic:
http://www.airliners.net/open.file/229226/LI KNOW this is is far from a perfect explanation. So any member are more than welcome to provide additional information.