Final answer:
Lamellipodia are the thin sheet-like structures that fibroblast cells extend during cell crawling to facilitate movement along surfaces.
Step-by-step explanation:
The thin sheet-like structures that a fibroblast regularly extends during cell crawling are called lamellipodia. Lamellipodia are temporary extensions of the cytoplasmic membrane that help with cell motility and allow fibroblast cells to move along surfaces by extending thin filipodia into the direction of movement. These thin extensions are made up of actin filaments and are involved in various processes in eukaryotic cells.