As pointed out in comments and other answers, pointer trails were originally "intended for" and "especially useful if you [were] using a liquid crystal display (LCD) screen" in Windows 3.1.
LCD monitors at the time were mostly passive-matrix, whose typically slower response times meant your cursor didn't have time to get redrawn as it moved across the screen. Pointer trails helped ensure the pointer didn't just disappear from the screen as it moved.
The pointer trail is no longer necessary for modern active-matrix LCD screens, but the feature has proven useful for accessibility. It helps people with visual difficulties to spot where the pointer is on a large screen by emphasizing its movement and leading you to its current position.
Here's a description from the UK National Health Service:
The standard mouse pointer is not very easy to see and many people find that they lose it as they move it across the screen. As well as enhancing the appearance of your mouse pointer you can also apply mouse trails. A mouse trail consists of just that - a trail of mouse arrows that fade away as you move the mouse across the screen.
A simple Google search for "pointer trail accessibility" shows instructions on how to set it for people with visual difficulties from a number of sites.
As to evidence of its usefullness, the only accessibility study I'm finding off-hand that discussed mouse trails doesn't make the results publicly available.