I believe you are referring to 'Average Costing' scenario because cost_quantity_layers table is used for this particular costing method as the cost of item gets updated with every receipt done in the inventory. These receipt quantities are stored as the 'layer_quantity' along with the 'create_transaction_id' column, which refers to the transaction id that created this layer quantity.
The significance of this 'layer_quantity' is that it is used in re-calculation of the average cost of the item after every receipt (or issue) transaction. Because the new average cost is calculated as
Average Cost = ((Transaction Cost * Transaction Quantity) + (Current average cost * Current On-Hand Quantity)) / (Transaction Quantity + Current On-Hand Quantity)
And here the Transaction Quantity is nothing but the 'layer_quantity' which is stored in the cst_quantity_layers table.
I hope this answers your question.