Why is it important that glucose’s third OH group points to the left?
This is the concept called stereochemistry.  

Each carbon with 4 bonds has an approximately tetrahedral geometry.  We assign a configuration to the situation by numbering the substituents in terms of priority. Hydrogen is lowest.  Oxygen is highest.  The top carbon is second, and the other carbon is third.  We then trace a route from 1 to 2 to 3.  This would be a clockwise circle, and we would call this configuration S.  If we switched sides between the H and the O we would follow this circle widdershins and call the configuration R.  So the substituents can't be exchanged because the configuration would change.

So what?

When there is only one of these tetrahedral centers (called stereocenters) in play for a situation, it does not matter at all which one you have.  But the moment a second stereocenter comes into the picture, chemical properties begin to change.  A fairly tractable analogy is feet and shoes.  When you aren't wearing shoes, your left foot and your right foot are about the same.  But when you try to put shoes on, putting the right shoe on the left foot is slightly more difficult than putting the right shoe on the right foot.  In this loose analogy, the 'reaction' of putting your shoes on is slowed based on how the stereocenters of foot and shoe interact.

Onto glucose ...  Because there are 4 stereocenters in glucose, it has a distinct shape from its isomers.  The other chemicals in your body also have their own shapes/configurations.  Glucose reacts slightly differently than other sugars in the body because of the way these shapes fit together.  Therefore you need to keep the configurations known and well marked.

Most people (about 94% of the rest of you) don't intuitively see stereochemistry concepts and need to make models.  However, pragmatically, if you can take this explanation, and remember that 'it just matters' to keep the notation consistent, you can probably get through most of biochemistry.  

If you want to make models, at your next wine and cheese party get some toothpicks, and two pieces each of four different kinds of cheese.  Put four of the cheese chunks on the end of the toothpicks, and then stick the tooth picks in a sausage or something.  Then make an exact copy.  After that is done, exchange two of the cheese chunks on one model and investigate what you have.  There should be no way you can twist or turn or rotate one model to have its kinds of cheeses in the same orientation as the other.  Once you have done this, the following picture will make much more sense: