This is a quilting process where each block is quilted separately then attached by sashing. There are many ways of doing this. My sashing strips never lined up exactly on both sides. So I always prefer hand stitching one side of one strip. The rest is always machine stitched.
I have made this type of quilt from left over blocks (I do get carried away). I lay a block on top of a piece of bat just a bit larger, place that on a piece of backing fabric the same size as the bat. Then quilt. Trim the bat and backing to make a perfect square. When enough quilted squares are made for a quilt, I then sash them together. All that is left is the binding.
The method I'm showing uses strips from my scrap pile.
The blocks were made by placing a triangle on the top and bottom of a batting square. Then a strip of fabric is placed at the edge of each triangle. Sew the strips to the triangles (which holds both triangles and both strips down). Flip the strips over, Now there is a triangle and a strip sewn to each side of the bat. Add more strips in this manner and this is what you get:
To join the blocks together you need a 1 1/2" strip of fabric for the top and a 2" strip of fabric pressed in half (making it 1" wide)
Next pin the top sashing strip to one side of of your first block. At the same time secure the raw edges of the bottom folded sashing underneath the same side of the block. Sew the two sashings to the block.
Leave the folded back sashing as is for now. The top sashing is pressed over. Now pin the second block to the raw edge of the top sashing. (Do not attached the folded edge of the bottom sashing.)
Keep adding blocks until the quilt is the size you want. All that is left is sewing the binding on.