A few 'trade associations' are little more than commercial companies who permit their members to use the the logos of those 'associations' in order to try to convince potential customers that they are dealing with a 'professional' trader. Such 'associations' will be run by the directors of those companies, rather than by people elected from within their membership.
'Proper' trade associations are formed by (and then run by) people working within the same trades who believe that 'being part of a club' will offer certain benefits to their members. Those benefits will vary from one association to another.
For example the Cutler's Company has (since 1624) "sought to maintain the standards and quality of Sheffield manufactured cutlery and steel products and to promote the name of Sheffield".
More recently formed associations often seek to provide a system whereby the public will know that they're dealing with a properly trained and accredited trader (sometimes providing an arbitration service for dealing with disputes). For example, I've often recommended here that anyone seeking an aerial fitter should look for the 'CAI Plus' logo. That's because of this:
http://www.cai.org.uk...the-cai/about-the-cai
As I'm guessing that it might be relevant to your question, here's what the SIA says that it does:
http://www.stoveindus...e_sia/our_mission.php
(I note that the SIA website names their chairman but no other officials. If I was considering joining I'd want to know whether the 'chairman' is simply the guy who created the SIA - and who can't be removed - or whether there's a proper constitution, with an elected committee).
Chris