The thin layer of fat that surrounds the cell is called the plasma membrane or cell membrane. While it's not entirely made of fat, it does contain a significant portion of phospholipids, which are molecules with a phosphate head and two fatty acid tails.

Here's a breakdown:

* Plasma membrane: The outermost layer of a cell that controls what enters and exits the cell.

* Phospholipids: The primary component of the plasma membrane. They form a bilayer, with the phosphate heads facing outwards towards the watery environment and the fatty acid tails facing inwards, creating a barrier.

* Other components: The plasma membrane also contains other molecules like cholesterol, proteins, and carbohydrates.

While the plasma membrane is sometimes referred to as a "fatty layer" due to the presence of phospholipids, it's important to remember that it's a complex structure with various components that contribute to its functionality.