Its importance rests upon the fact that occupiers of buildings were liable for the tax (whether or not they owned the property) and that classes of people who could not pay were listed as being exempt. So (almost) every head of a household in the country would have been recorded in one way or another.
For detailed background, look at the Family Search Research Wiki entry which includes a link to a UK National Archives slide presentation. The TNA also provides an excellent research guide called Taxation before 1689.
A very good entry point to surviving records can be found at Hearth Tax Online which has both name lists (that you can download and browse) and maps. This is an academic site supported by Roehampton University but it is a rich resource for family historians.
There are very limited Heart Tax records held by the major subscription sites. If you are interested in Northamptonshire try Find My Past or for Suffolk look at Ancestry.
Because these records are so ancient and so important, lots of historians have worked on them to produce derivative works. You may find useful sources by searching the major repositories of out-of-copyright books such as Google Books, Archive.org or the Hathi Trust.
Any group member who might like a quick quiz to remind you of the main points covered by Les can go to http://quiz.al and enter an invented user name (it can be one you used last year, or you may create a new one) and the class code afq457.