Sure. Cloudflare recently launched their public DNS at 1.1.1.1
This link will give you some good info and basic understanding on how it works:
https://www.cloudflare.com/learning/dns/what-is-1.1.1.1/
I linked this page instead of Google's as they don't get too technical about it so for anyone unfamiliar with the subject it should not be too hard to understand.
Back to Google. They have been offering the same thing for ages:
https://developers.google.com/speed/public-dns/
Now, as you can see using a third party DNS resolver in a perfect world speeds things up, is more secure etc. Over time more and more people have started using Google's DNS instead of their ISPs. Now imagination a world where everybody is using them. It does give them a lot of power over the way domains are resolved. We all (well the mass) blindly trusts them so what's to keep them from abusing this power?
It's not the end of the world if they would and It's not an imminent concern of mine cos if they did mess with it it'd be a huge scandal. But didn't we think exactly the same thing about Facebook up untill a couple of years ago?
Taking into consideration they are also invested in the internet's physical infrastructure, are a registrar, and basically 'own' all data in the world you can see that we/they created the ultimate setting for global power over the internet.
That being said, I am typing this from my Android phone and will be using my Chromebook for most of the day but I think it's important to realise (at least) the vast power we are willingly giving to companies like Google.