Semantics are the meaning of words. HTML is a language, and the words in it have their own meaning too.
The semantic meaning of a p element is paragraph
Div is the only one that does not have a semantic meaning
Using proper semantic html will ensure best experience for the users with assistive technology, like screen readers, and it can also improve search rankings
Using proper headings is important. You will rarely have more than one H1 heading on a page
You shouldn't skip from H1 to H3. You can however have multiple same level headings of the same level next to each other.
It may be tempting to use a certain heading element because of it's styling. Instead, you should use the appropriate element and use CSS styling to achieve the desired effect.
Proper structure is also important for SEO and screen readers