Here's an easy way to think of it:
If I draw a quarter of a circle on a piece of paper, you could look at that quarter arc, complete the rest of the circle, and point out the centre pretty easily.
When you turn on the IRS, and the aircraft is stationary on the ground, then the only movenment the aircraft senses is the rotation of the earth. So as the IRS's plot their position, they start to "draw" a cirlce. Once they have drawn enough of a circle, the computer can complete the rest.
The size of the circle tells the computer the latitude of the aircraft, while the centre of the circle is true north.