'Related topics and semantically connected keywords,' does not refer to the things that come up during a traditional keyword research process. The idea here is not to say, "What other things are people searching for?" This is really about two different, unique kinds of use cases or extractions for keywords.
1. What are the keywords, unique words and phrases that are used on pages and paragraphs which contain the query across the web?
2. What are the terms and phrases that are used by majority of the pages that rank for that particular query?
1. Keyword: "Cycling Tour" In order to make the page and site more relevant, and to rank better for this keyword, using certain words and phrases on the page where we are targeting "Cycling Tour", is very important.
Google might look at a page that's ranking for "Cycling Tour" and say, "Gosh, it's weird that this page doesn't have this keyword on it. We would expect that a page that's targeting 'Cycling Tour ' should have these things.
So we have to find two things: In the top 10 or top 20 results that Google already has for "cycling tour" we have to find out what are the words and phrases that appear on those pages most frequently? And across the entire web, what are the words and phrases that are used most frequently on pages where the phrase "Cycling Tour" is present?
For example, the word "adventure" is used across the Web on lots of pages that contain "Cycling tour" which makes sense. Lots of adventures that call for cycling tour have the word "adventures" on the page. But those aren't necessarily the ones that rank very well. Its position is high on the "Yes, used across the web" but low on "Used by pages that rank well".
2. Keyword: "Game Development" If we want to rank better for Game development keyword, we should use certain words and phrases on the page where we are targeting "Game Development".
In the top 10 or top 20 results that Google already has for "Game Development", we need to find which words and phrases appear most frequently on those pages.
So if we have a page that's targeting Game Development, we have to think about: What are the topics, concepts, words and phrases that Google is looking for and the users searching for? Topics could be on the lines of 3D Game Development, 2D Game Development, 3D Game Art, Game Animation Studio, Game Concept Art etc.
Using these words on the page can help us to become more relevant.
Not every one of these semantic and related topics is going to be a good choice. We have to use good judgment and traditional metrics that are used for keyword search volume, difficulty, opportunity to discover the right ones.