The IRS can figure out our latitude without any external input. It cannot figure out the longitude. This we have to give it. We in fact give it both.
The earth is revolving. The IRS is sensitive to all acceleration so it can feel the acceleration around the earths axis. This is of course the axis between true north and south. So by measuring it's speed through space it can work out it's distance from the axis or rotation, i.e. it's latitude on the surface of the earth.
If it is sitting on the equator the speed through space would be fast and therefore the forces it feels strong.
If its sitting very close to the north or south pole the speed through space would be slow and the forces weak. Too close and it's not sensitive to align at all.
The alignment phase is really only finding out where the North south axis is. We then tell it what the longitude is.
When it knows lat and long and is aligned any new accelerations are converted to velocity of the aircraft and the position updated.
IRS 101