What is that companies do that promise to improve a person's Web site ranking?

Good to be skeptical . . . .

It depends on what your goals are for your site. If it is your goal to appear higher than some other sites in more Google search results for “integral calculus for kids” or something, and you’d pay someone to help achieve that goal, then they may be able to help you out there.

If you’re not looking to give them money to improve that, then no.

What they’ll do is use their latest information on the current way Google analyzes web pages and chooses to offer them to people, and suggest changes to your page like adding meta tags to the HTML that don’t display but do get noticed by web crawlers. It used to advice like “add relevant words like math and calculus and homework help, and also popular search terms like Fortnite and Pamela Anderson and hot”, but it’s changed over the years. I assume there are newer tricks these days.

Generally they exaggerate and lie. And charge you for it.

https://en.wikipedia.org/wiki/Search_engine_optimization

Of course, it can be done. It isn’t too difficult either, as long as your website is not competing with a mega ranking, globally famous competitor. I can understand your skepticism but just don’t brush away all the claims made by the company that contacted you. I am from that industry, so, I do know that the person who contacted you would have done a basic test on your site to determine its status and marked down things that can actually be done to benefit you (and them too obviously). It is a common practice in this industry to ‘cold call’ potential customers. The companies don’t even bother approaching a customer, if the basic test turns up unfavorably. In all probability, the guy who contacted you, did actually have concrete plans to imrove your site’s visibility and optimization. As business owners, even they need something to show you at the end of the month, in case you opt for their services, right? So, yeah….since you said you aren’t too bothered with the site, it is logical that you won’t take up their offer but I thought I’ll leave this answer for the benefit of others, who might share the same skepticism.

@AK That is an awesome answer. As somebody active in this relatively new field, can you help me out with the following specific questions:

1. Does Google prioritize paying advertisers?
2. Is SEO basically a trial-and-error technique, now that Google and other search engines have stopped sharing their algorithms?
3. Is there a way of prioritizing a particular website for a home for sale?

@crazyguy
.1> Technically, it doesn’t prioritize advertizers. Well, it does display ads above the fold but the suffix “Ad” is its technical loophole. People do know that they are ads, so, big G escapes. Even if they don’t display above fold ads, Google has other ways to target you with advertizers. Let’s say you search for “boots” through the search engine, Google immediately taps into its advertizer database and links it to boots advertizers. From then on, every site you visit will miraculously have boots related ads. Every site that has google ads enabled on it, will show you your product. As a consumer, you won’t mind it either because you want boots and searched for them…those ads will eventually lead you to a place where you can actually buy those boots.But as a website owner who sells boots, this system is grossly injust. I won’t get anyone to my site, unless I spend 1000s of dollars on optimization or become an advertizer myself. That is the diabolical world we currently live in. Google rules over all of us.
2>Google never shared its algo. It only shares info on how some parts of the algo work. Even with that, they obfuscate and throw in many red herrings. People can reverse-decipher some parts of its algo (or so they claim) and that is why you see so many optimization theories floating on the net. Some of them are genuine. SEO is not trial and error, its processes are. If you want to optimize for keywords which is one part of SEO, you can do it in umpteen different ways. People keep discovering new processes and that takes a lot of trial and error. If you stick to tried, tested and proven methods, you won’t need to trial and error (you can leave that to others with more time and money).
3> Your best bet would be to not target google search at all! There are other ways to bring in target customers. Social media platforms are more effective…I mean to say, they are faster in bringing in potential buyers, especially home buyers. That is a big niche and you won’t be able to compete with the corporate heavy spenders who hog the search engine top folds. FB and its pals will bring in target audience for you.
Edit: Sorry, I forgot to say local marketing. When you target social media for buyers, always filter it down locally. Target people in and around the place where the house is. Don’t broaden your target audience, funnel it down.

@AK Thanks a lot.