The visual divider is a layout element that helps to separate pieces of content into clear groups, sections, options, or parts. This way, it helps a designer organize the page according to the typical patterns of visual perception and makes the layout clearer and more digestible for users.
Together with other elements on the page, dividers play a great role in setting up a solid visual hierarchy. For example, with them, users can easier define the relations of content, like if the pieces of content are the same, similar, or related; if any of them is subordinate to the others, etc.
Dividers are also important for usability: in many cases, they create visual containers that look clickable or tappable, which is particularly crucial for mobile interfaces.