Could somebody explain a little bit why they need 2 separate GPS and 2 separate IRS?
Because airliners falling out of the sky or disappearing without a trace is not acceptable from either a political or financial standpoint. Stuff fails and so backups are needed to keep the flight on-track when it does.
Having two systems of each type makes it easier to automatically detect failures, having two different types of system helps avoid systematic issues that might affect two systems of the same type equally.
Follow-up question: this same website states: "POS INIT is used to enter the aircraft position into the IRS's for alignment". What is meant by "alignment"?
Inertial navigation relies on a double integral. The sensors measure acceleration, the acceleration must be integrated numerically to get velocity, and velocity must be integrated numerically to get position. Gravity and rotation complicate the picture even more.
The trouble with integrals and particularly double integrals is they tend to compound errors over time. A constant error in acceleration translates to a linearly growing error in velocity, which translates to a quadratically growing error in position.
So, to maintain acceptable accuracy, intertieral naviation systems must be frequently re-set to the aircraft's real position while the aircraft is staionary on the ground.