Why are there two IRS switches on the 737NG?
Inertial Reference System is a solid state set of 3 ring gyros which navigate using dead reckoning.  The system measures accelerations in  and rotation around each of the 3 axis so can calculate where it is by adding how much it has moved to the initial position.

A simple example:
The aircraft is stationary pointing North.  Over a 10 minute period, it measures the accelerations in the X and Y axis and calculates that is has moved +100 kms in the X axis (i.e. North) and +100 kms in the Y axis (i.e. West).  By simple trigonometry, we can calculate that the aircraft is approximately 141.4 kms on a bearing of 45 degrees from it's initial position.

The gyros must be aligned with the aircraft frame of reference when it is stationary.  This is the "alignment" process and generally must be completed before the aircraft moves.  It may also take inputs of the current position from a manual keyboard or from some other system, e.g. GPS.

More modern IRS fits can align when the aircraft is moving, taking an updated position from GPS.

There are 2 systems on the 737, simply for redundancy.

This slide show gives a good overview.