A balustrade is a row of spindles that support a railing. You're especially likely to notice balustrades on balconies or bridges.
A small wooden or stone pillar or column is a baluster, like the balusters that support a stairway railing. A whole row of balusters lined up together comprise a balustrade. Balustrade is a French word that's rooted in the Italian balausta, "flower of the wild pomegranate," which has a double-curved stem shaped like a baluster.