In Demon Slayer, there are;
five fundamental breathing styles; these are water, flame, wind, stone, and thunder. There are many derivatives, but the main character Tanjiro is taught that they can all be traced back to these, which can subsequently be traced back to sun breathing.
See the wiki for more information.
When watching the show, they are often represented visually, but so far (and from my research), I can't seem to figure out a reason why it would be important for them to be represented in a visual way.
Thinking about it from the aspect of someone who is watching the show out of context, they might believe that some characters in the show;
have elemental powers when these are simply breathing techniques.
Is there any known  significance to the visual display of elements in Demon Slayer?
1: Here, known can be something I missed or misunderstood on the wiki, or an official source such as a statement by the creators in an interview; it should be supported with citations and not be an opinionated answer trying to infer creator intent.