So does NowFloats do search-engine optimization (SEO) for my business website?

Technically speaking, yes. NowFloats takes care of the SEO for the website and the content you create on it. Normally businesses have to fork out money to digital agencies to do the SEO for the website - to maintain it on a monthly or an annual basis.
However with a Boost business website, you get the SEO built-in already. So all you need to worry about is what you want to tell the customers about your business.