Blueberry shrub is a sweet and sour mixture of fresh blueberries, cider vinegar and sugar that is strained and cooked briefly. While shrubs can be alcoholic (where the vinegar is replaced by alcohol, and have citrus as a base) or non-alcoholic, all shrubs have a sweet-tart flavor to them.
The word shrub comes from Arabic, and was first used in English in the mid-18th century to describe blends of alcohol, citrus juice and peel, and other spices that were sweetened with sugar, then filtered and bottled. Before the advent of refrigeration, these drinks could be preserved throughout the summer months without spoiling.
Shrubs are very similar to gastriques, which are sauces made from caramelized sugar deglazed with some sort of acidity.