Balsamic Vinegar Reduction is a great "go to" when you're looking for something to jazz up a dish or give a dish a little flavor boost, it's also a great food decorating tool.
It can be kept in the fridge for ages and doesn't go off if kept at the right temp.

Balsamic is a perfect accompaniment for cheese, especially parmesan or hard cheeses and can be drizzled over hot or cold alike. 
It's also the perfect accompaniment for tomatoes, dried meats and most other vegetables.
A crafty spoon of balsamic reduction makes ordinary food look like a superstar.

This reduction is easy to make (of course!) and doesn't take a long time to cook but I'd recommend making it with enough time to let it cool before you use it.
Don't waste your money on expensive vinegar for this as the "good stuff" will be wasted flavor wise.
You're best to use the good stuff natural and without any additives.

As for the other major ingredient in this reduction, wine, don't use expensive wine but likewise don't use old or "off" wine. 
The rule of thumb when cooking with wine is:

If you won't drink it, don't cook with it

Use only good, freshly opened wine and the fuller bodied the better flavor wise for this dish.