The empty P element represents a paragraph. The exact rendering of this (indentation, leading, etc) is not defined here, and may be a function of other tags, style sheets etc.
You do NOT need to use <P> to put white space around heading, list, address or blockquote elements. It is the responsibility of the rendering software to generate that white space. An empty paragraph has undefined effect and should be avoided.
Typically, paragraphs are surrounded by a small vertical space (of a line or half a line). This is not the case (typically) within ADDRESS or (ever) within PRE elements. With some implementations, normal paragraphs may have a small extra left indent on the first line.
<h1>What to do</h1> <p>This is a one paragraph.<P>This is a second. <P> This is a third.
<h1><P>What not to do</h1> <address><p>I found that on my XYZ browser it looked prettier to me if I put some paragraph tags</address> <p> <ul><p><li>Around lists, and <li>Inside headings. </ul> <p> <h2>None of the paragraph tags in this example should be there.</h2>