Hello,
I suppose you have an aircraft which is fitted with dual FMC. So I can't tell you much how it works. But maybe this will help a little bit...
On a single FMC aircraft, FMC position is a computer generated position. How it got to that position?
1) On the ground, first initialize (align) the position to your parking bay. While taxiing, FMC will take IRS L usually as its source of information (it looks at your g/s and heading and senses acceleration)
2) On takeoff, it will update itself to the runway position. If you do intersection takeoff, put in the runway shift so it will shift its position to runway position + runway shift
3) After airborne, within 25 nm of a VOR, FMC position will be updated to VOR radials, if it senses that the VOR is giving out correct info. Otherwise, if lets say you put in the wrong runway for the takeoff, it will now be confused. The FMC position and the IRS position is so far out, it will ask you to verify its position. In that case the FMC position can be updated to the IRS position that closely matches raw data (VOR/DME in fix page which is FMC position and the VOR/DME of the station). Look at the arrow symbol and its distance, that is how far away the IRS position as compared to FMC position. If you doubt your ability to verify the correct position, autotune one of your navaid and let the agility tuning do its work to bring the FMC position to what is most accurate.
4) The FMC position will be updated based on either GPS, DME/DME, VOR/DME, LOC/DME if within 17nm from touchdown or VOR radials if within 25nm away from a VOR station. The confusing thing about this is if IRS NAV ONLY msg comes into the picture. Why don't the aircraft turn to the IRS position? The FMC position is now based on its last known position plus whatever is the difference between the FMC position and the IRS L position (usually) and the difference is maintained throughout the flight until it receives another update either from GPS or ground based aid. If for some reason you do not trust the FMC position in the air while there's no updating, the FMC position can be updated to the IRS position as a temporary measure, until it gets another update.
Hope that helps...