I recently did a search with my website's name,
"subscriptionconnection" as the search term.  I received back 8 SERPs.
 Of those nearly 80 listings, only about 5 were relevant.  I am
unfamiliar with the others, they have no relationhip to
"subscriptionconnection" and often, while the descriptions often are
from pages in my site, the url links are to places that are
competitors.  Can you explain what is happening here?

They appear to be search results shwoing pay-per-click ads from
Kanoodle. If your site is advertised on Kanoodle, then that will be
why.