The <p> starts a paragraph and </p> ends a paragraph.
The <br> starts a line break and </br> ends one.
The difference between the two = the paragraph is a bigger 'space'.
What moshu was saying is that <p> </p> is only putting a large gap of space.
So, for sake of argument, <p></p> leaves a double space line, <br> </br> leaves a one and one-half line space and not using either (or only using <p> or <br> is simply single spacing).
You only have to close these tags (meaning </p> or </br>) when you're ending or open with them (<p> <br>) when you're starting - and need a new paragraph or line.