What paragraphs accomplish
Text that isn't split up into paragraphs is often referred to as a "wall of text" and can be very difficult to read. Paragraphs are used for a few reasons: Organization, pacing, and to give the reader a chance to pause, similarly to what the end of a sentence does.
Paragraphs exist to group sentences on the same topic together. For example, sentences that all explain why a tree was planted might be grouped into a single paragraph, then sentences describing the tree might be a second paragraph.
However, when paragraphs get too long, it's usually a good idea to break those up, too.
Some writers have a habit of writing paragraphs of roughly equal length. This generally will put the reader to sleep, so it's a good idea to vary paragraph length occasionally. You can think of a paragraph as analogous to a sentence, but instead of being made up of words, a paragraph's components are sentences. And just as sentences have their own rhythm, so do paragraphs.
"Dialog is a special case," said Mary. "The convention in English is that, within a single paragraph, there's only one character speaking."
Joe thought for a minute, then asked, "does that mean that when a new character is speaking, there should be a new paragraph?"
"Yes," said Mary.
Paragraph breaks should be visually clear. There should either be white space in between paragraphs, or each paragraph's first line should be indented on the left.
On the web, it's generally easiest to type an extra return between each paragraph to create white space. There are solutions within HTML and CSS that will accomplish the same thing, however.