Bullet points are, in some ways, the perfect tool for writing articles.
A good bulleted list plays a number of roles within your article; from aiding with the reading of the article and getting important points across to your readers, to making the article a far more inviting to read in the first place.
Bullet lists are a great aid to:

• Readability: Bullet-point lists tend to add a lot of whitespace around the text effectively breaking up blocky text, and helping to reduce the 'overwhelm' effect of too much text.
  
• Scanning: Bulleted lists enable the reader to scan your article and find the most relevant pieces of information fast, and with the hectic lives and easy access to information that's what most readers look for when searching for information in articles.
  
• Comprehension: Presenting lists, in no particular order, in small chunks helps the mind comprehend the grouping of information - a bullet list is nothing more than a collection of somehow-related items.
  
• Sub-bullets can also enhance comprehension because there is an instant hierarchy - it's obvious that this bullet about sub-bullets is related to the topic of Comprehension, for example.
  
• Highlighting Key points: Note how each bullet in this list begins with a bolded statement? This helps to highlight the point of the bullet point, making it easy to see the key point of each one without needing to read the text explanation that expands on the point.
  

Bullet lists come in two formats - ordered (using numbers or letters) and unordered (using the same bullet icon for each point):

• Ordered Lists: The ordered list is used when the list of related items has a progression, or an order of some sort, such as a How-To type list where you want the reader to follow the points in a specific order to obtain a specific result.
  
• Unordered List: When you have a group of related items, and the order presented or read doesn't affect the outcome, then an unordered list works just fine (as in both examples used so far in this article).
  

A bullet point should never be more than a single paragraph, a single idea or concept.
If there is more to say than you can fit into one paragraph then the item might not be suitable for a bullet list, or you may want to look at using sub-bullets to get the additional information across.
Lengthy multiple paragraph bullet points detract from the main benefits of using a bullet list in the first place (see the first list above).
You may also have noticed that prior to each bullet point list there is an introduction statement explaining what the list is for, which sets the context of the list to your reader and lets them know what they are about to read.
Particularly on the Internet, people have an almost instant need to know what they are looking at, and with ever-decreasing attention spans due to the instant availability of more information being available on the Internet it's important to get your message across as soon as possible, in an easy to understand fashion.