Semantics is a branch of linguistics concerned with deriving meaning from words. Semantically related keywords are simply words or phrases that are in a related to each other conceptually.
For example, for a keyword like “search volume,” some semantically related keywords could be:
For a keyword like “cook asparagus,” some semantically related keywords could be:
“Semantic search” is the idea that when modern search engines look for webpages to rank, they don’t only look for matching keywords, but they attempt to identify the intent and deeper meaning of a search based on each of the words used in the query.
Essentially, Google is trying to understand language on a higher level in order to serve more accurate search results for a wider range of queries.
From the SEO side, having more semantically related keywords means that your webpages provide more contextual background on a topic and therefore they can perform better in search results.
Google will be able to make connections between the semantically related topics that your content covers and understand the bigger picture of how your information answers the questions that are being searched.
For more explanation about semantic search, Search Engine Journal's article: What is Semantic Search and Why Should I Care?