Wearing socks to bed can increase blood circulation to your feet, which causes blood vessels to widen (aka vasodilation), according to research.
As a result, your core body temperature is lowered. Your circadian rhythm (i.e. your internal body clock that controls your sleep-wake cycle) helps to regulate several bodily functions, including your internal body temperature, "which is generally set by the environment," according to the American Sleep Association.
So, since sleeping with socks on can cause blood vessels in your feet to widen and release heat from the body, that means this simple act can essentially encourage your body to initiate the cool-down process for your circadian rhythm that ultimately gets you to sleep.
One tip. Have a pair of big, fluffy socks that you designate for sleep. Don't wear tight socks with elastic or rubber bands, loose is better.