"Excess fat deposits" refers to the extra amounts of fat that are stored in certain parts of the body. It means having more fat than what is considered healthy or necessary for normal functioning. Full definition
This means (among other things) having the ability to create a portable energy supply in the form of excess fat deposits. (muscle-fitness-training.com)
What if your man tits are caused by excess fat deposits? (gynoguide.com)
According to Munsey Wheby, president of the American College of Physicians, excess fat deposited in the liver is thought to trigger the production of inflammatory molecules that damage cells and ultimately — if left unchecked — lead to cirrhosis. (discovermagazine.com)