a.k.a. Seagrass Glass
This is a woven raffia-covered glass set for water service.
It is a perpetually popular type of serving set that has been made for decades with slight changes by different manufacturers and under different brand labels.
The raffia serves a utilitarian purpose to prevent slick glasses from falling out of one's hands. The same reason that Plantation Rum puts raffia over its rum bottles.
One famous example of this style are the "Trader Vic's Hot Buttered Rum Glasses with Basket Holder" which are wrapped in the same kind of matching raffia.
Most recently this set was produced by Williams Sonoma. Their "Weave Wrapped Glassware collection" includes four-inch tall double old-fashioned glasses with a 12-oz. capacity; six-inch tall highballs with a 12-oz. capacity; and a 10 1/2-inch tall carafe with a 35-oz. capacity.