Label unwind direction is simply the way in which a label unwinds from a roll. This is most easily explained by looking at the diagram below. There are four unwind directions. You can see that unwind direction #1 is when the top of the label comes off the roll first, #2 has the bottom edge coming off first, #3 is the right edge and #4 is the left edge.
Now, why is it important? Well, it is usually only important if you are having your labels applied by machine - if you are hand applying your labels then unwind direction typically does not matter. So, if you are applying your labels by machine, or having a contract manufacturer apply the labels then you will need to know the unwind direction. Most labeling machines will only be able to work with one unwind direction for each type of container.
One final point, if you are applying labels by hand now, but you may want to have them machine applied at some future point it is still good to consider unwind direction.