There are lot's of reasons:
Pure imbalance with equal stiffness in both directions may generate approximately equal vibrations in both horizontal and vertical directions.
The dynamic stiffness may be radically different in the horizontal and vertical directions and each direction also has different resonant frequencies. Sometimes 1x is higher in the 1x direction and 2x is higher in the vertical direction due to resonance at one of those frequencies in one of those directions.
Misalignment can generate a number of complex patterns:
One is an oval-shaped orbit which may have it's access in either plane (H or V) or in some 3rd radial plane in between.
Starting with two readings gives us the info we need to start to sort thru some of the above possibilities and more. Additional info is sometimes needed (phase relationships). Probably most important, these numbers allow us to begin to visualize the way the machine is moving in space and time.
bpr18,
You need to know what levels of vibration are in each plane; horizontal or vertical. By using vectors, the counter measure for dynamic balancing can be calculated. Another reason - take for example a shell bearing on a modeartely sized fan. The bearing might be out of round (or oval) which would give higher levels of vibration in the major axis of the ellipse than on the minor axis. The different planes can indicate looseness in particular areas.
Do hope this brief explanation helps.