Waves 1 and 2 are just the number of larghe scale planetary waves that are affecting the stratospheric vortex at a particular time.
If you imagine that the vortex is a balloon ( a rough analogy here) and you place pressure with 1 finger on that balloon then you will create a distortion similar to 1 wave or wave number 1. If yo place two fingers at opposite sides and apply presssure then that is akin to 2 waves - wave number 2 . And 3 fingers at different points a three wave pattern will be created. We are used to waves with a far smaller wavelength - such as the number of Rossby waves travelling around the troposphere - but the number deflecting the stratospheric vortex at any one time is far smaller.
Of course the polar strat vortex is more cylindrical in shape and the waves are created by higher pressures throught the depth of the stratosphere. Going back to the balloon scenario it is easier to imagine how wave number 1 can create a displacement type of event on the vortex and wave number 2 a splitting type of event.
The precursors to the waves are normally higher pressures around mounrtain ranges that can divert a tropospheric wave into the stratosphere creating a mountain torque evnt in the process. There are only so may mountain ranges in the NH that can create this which is why we don't have more than a wave 3 event at any one time.