Filet Crochet is a kind of simple lacy crochet. Usually worked with Double Crochet and Chains.
Below is a closeup of the rose pattern:
Begin with chains to the desired length. The leave 2ch and start working 1dc in 3rd chain from hook, then ch1, skip next ch, then work 1dc in next ch in base row - thereby forming a mesh pattern for the base.
Then pickup a cross stitch design (the above rose is a cross stitch pattern too) and work DCs to cover the design and the background can be worked in the mesh pattern