If you want to try for yourself:

Pick up a book. Hold it in front of you, upright with the cover facing you. Now think of fixed x, y and z axes in your room, with the same orientation as in Poser: x pointing to the right, y up, z in your direction.
Rotate the book by 45 degrees around the y (up) axis. Then rotate it by 90 degrees around the x axis. Remember its position.

Now put it back in the initial position. Rotate it by 90 degrees around the x axis. Then rotate it by 45 degrees around the y (up) axis. Note how you get a different result than before - rotation order does matter, even without a single line of code.

We were just using world space rotations, now let's try if local axes are better. Let's not use a book but your right hand thumb, index and middle finger - forming a right hand coordinate system with the thumb being the x axis, the index finger being y and the middle finger being z, see the picture.

Now rotate 90 degrees around the thumb (x), so that your palm points upwards and the index finger away from you. Then rotate 90 degrees around the index finger (y), so that the middle finger points to the left and the thumb points up. Remember that position.

Back to the inital position, x right, y up and z at you. Rotate 90 degrees around the index finger (y) - thumb pointing at you, middle finger to the left. Rotate 90 degrees around your thumb, same direction as before, putting your hand in a position with your index finger pointing to the left and the middle finger upwards.

Again, rotation order matters. We did the same rotations as before, only in different order.