You use h3-h6 as subheadings.

For example, you write an article about widgets and you talk both about three types of widgets and three ways to do something with them.

h1 goes for the article title

h2 goes for the three types of widgets

h3 is used for subheadings in the h2 sections to show the three ways to do something with widgets (buy, tune, store, for example).

h1: Widgets, The Complete Guide
h2: Blue Widget
h3: How to Find a Blue Widget
h4: Local Shops
h4: Internet
h4: Local Communities
h3: How to Repair a Blue Widget
h4: Do it Yourself
h4: Find a Master
h4: Send to the Service Center
h3: How to Sell a Blue Widget
h4: Sell to a collectioner
h4: Sell to a specialized shop
h4: How To Sell on eBay

h2: Green Widget
h3: How to Find a Green Widget
h3: How to Repair a Green Widget
h3: How to Sell a Green Widget

h2: Red Widget
h3: How to Find a Red Widget
h3: How to Repair a Red Widget
h3: How to Sell a Red Widget

As you can see, such heading structure is pretty neat. I can foresee rare cases for the use of h4 tags, but the HTML specs have tags up to h6, which should work for really, really long and detailed articles.

As a side note, using words in h2-4 tags will help, because:
- it makes reading faster and allows the visitors to jump to the section they want and allows them to convert
- works for the search engines, who see the words your visitors use in your subheadings to show the page to them