My question is about how to influence the way google shows my page as a result, when someone searches form my store "tbl furniture".
Currently it looks like this
what I would like to have is just the link to the the website with the meta description,
without the results listed below that actually link to 4 other pages of the website, with no particular relevance.
What should I do?
There used to be a tool for supressing unwanted sitelinks in Google Search Console, but it's been missing for a while now. Some advice: http://searchengineland.com/google-search-console-removes-sitelinks-demotion-feature-261002
Even when it was available, it was like a whack-a-mole game where you'd demote a link and another would take it's place - usually even worse than the original because Google already thought the existing link was more relevant.
Best way to remedy is to investigate why Google may think the displayed links are relevant, and improve upon them to look better in SERPs. For example, change titles and meta descriptions to better explain what's on the page, or at least look more appealing to potential visitors.