Chain piecing is sewing many pairs of fabric one after another without cutting the thread between them.
For example if you need to make 20 half square triangles, cut your pieces, and put them in two stacks next to your sewing machine. Then take one from each stack, place them right sides together and sew, leave that set under the presser foot and take the next set, place them right sides together and sew them together. Leave the thread between the sets without cutting the thread.
When they are all sewn, take them to the ironing board, cut the thread between them and press.