This is all confusing the hell out of me. I'll use SO2 as an example. It has 3(3) - 6 = 3 degrees of vibrational freedom and it is in the C
2v point group. I read that if I count how many bonds are left unchanged by each symmetry operation I get a "reducible representation". It then says that when I find out what irreducible representations the reducible representation is made up of "this result tells us that there are two non-degenerate stretching modes, one of A
1 symmetry and one of B
2 symmetry."
I'm lost. I read that the A
1 (or A
2, A
3 etc.) label means symmetric with respect to the principle rotation axis (the z axis) and B
2 is asymmetric with respect to the principle axis. What does this mean with respect to stretching vibrations? Does this mean that A1 is the label for a symmetric stretch and B
2 the label for an asymmetric stretch? If so whats the difference between B
1 and B
2? In this diagram here:

I'm trying to figure out how the character table relates to the diagram but I'm having serious trouble. How does A
1 and B
2 represent 2 stretching modes of vibration?