Headings are used to set off and introduce different sections of a document. Headings go from the most important, H1, to the least important, H6. You can think of them as parts of an outline of your page. Here's an example:

<H1>Heading for Entire Document</H1>
  |
  <H2>First Main Section</H2>
  |  |
  |  <H3>Sub-Section 1.1</H3>
  |  |
  |  <H3>Sub-Section 1.2</H3>
  |
  <H2>Second Main Section</H2>
     |
     <H3>Sub-Section 2.1</H3>
     |  |
     |  <H4>Sub-Sub-Section 2.1.1</H4>
     |  |
     |  <H4>Sub-Sub-Section 2.1.2</H4>
     |
     <H3>Sub-Section 2.2</H3>

Here's the above example, using the actual HTML, so you can see the size of the headings.

Heading for Entire Document

First Main Section

Sub-Section 1.1

Sub-Section 1.2

Second Main Section

Sub-Section 2.1

Sub-Sub-Section 2.1.1

Sub-Sub-Section 2.1.2

Sub-Section 2.2

Headings can take the attribute ALIGN, with values of LEFT, CENTER and RIGHT. The default is LEFT. So, a Level 3 heading, centered on the page, would be defined by:
<H3 ALIGN="CENTER">Chihuahuas</H3>
The result would be:

Chihuahuas

It is undesirable to use H5 and H6 for two reasons:

1. H5 and H6 are usually rendered smaller than regular text, thereby taking away their importance and making them hard to read; and
2. a document with many sub-sub-sub-sections would be easier to read if broken up into smaller documents.

Also, don't use Headings to emphasize regular, non-heading text. Some search engines use headings to judge the important, key parts of a document, and excessive headings may water that down. There are elements specifically meant to give emphasis to text, and in the overall picture of HTML, you make stronger documents when you use elements for what they were intended.

Next: Paragraphs