Blocks of emerald are often used to store emeralds in a compact fashion. They are also commonly used as decorative blocks.
Beacons
Blocks of emerald can be used to "power" a beacon. The beacon can be powered by a 3×3 square of emerald blocks underneath it, and can optionally also include a 5×5, 7×7, and 9×9 layer in the shape of a pyramid under the original layer to increase the effects from the beacon. The layers do not have to be entirely emerald blocks, as they may also contain blocks of iron, blocks of gold, blocks of netherite, and blocks of diamond.