Wordpress Do I need to update WordPress?

I have developed the site is on WordPress 4.6.6 and I have often came across statements that for security purposes you must more or less regularly make the updates. The Webmaster of my website, on the contrary, says that there is no sense at all to the same after the upgrade appears exactly the same error.

So should I update or not? Does it have a significant impact on SEO, site security, web design, or anything else?

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Thanks for the suggestion Eva2000. I have hosted my site on Managed WordPress Hosting and my Admin says that we don't need to take care of this as everything is updated automatically. But I am a bit reluctant about this.

 

Spoke with the service provider and they say that we don't need to manually update anything as it is all done automatically.