Emerald Shards can be crafted into Emerald Pieces by right clicking with 8 of them in your hand. Similarly, 8 Emerald Pieces can be right clicked to create a vanilla Emerald, meaning it costs a total of 64 Emerald Shards to create a single vanilla Emerald. You can take 9 Emeralds and turn it into a Block of Emerald, using 576 total shards to make the block.
You can reverse-engineer Emeralds into Pieces, and Pieces into Shards by placing an Emerald/Emerald Piece (respectively) onto a Crafting Table. This is rarely useful, except in the case of very limited inventory space (if you are able to contain all the Emerald Pieces/Shards in a single slot), or if you are doing player-to-player trading online.
Emerald Shards are sometimes dropped upon the death of a mob as well as upon destroying the top layer of a Mystic Shrub. In addition to Emerald Shards, you may also find Emerald Pieces when breaking an Energized Mystic Shrub, or very rarely, a full Emerald.