Semantics
Semantics in the context of HTML refers to the use of the appropriate elements for the appropriate meaning. It is possible to make a web page entirely out of div and span elements. We can style this page to exactly match the normal browser style. In fact, most of the users of the web page would not notice anything that had changed. So the question is why would we want to spend so much time learning different elements. We could have easily learned only the two elements and immediately started cranking out web pages.
Search Engines
One of the reasons is that the web pages are visited not only by humans but also by search engine bots. These bots can understand the web page only when there is a proper and meaningful structure. In return, we receive traffic from these search engines. These users that come from search engines are important because they are actively seeking out our content. They are more likely to engage more with our content. This is only possible if the pages are well structured so that search engines can extract more meaningful information.
Accessibility
Another strong reason to consider sematically sound web pages is accessibility. There are many people who are not able to experience the Internet fully. They may be using alternative tools like screen readers for accessing the web pages. It is important to consider the needs of these users if you want to reach everyone. We should try to be more considerate of these people needs. This is where semantically correct web pages are useful. If the meaning of the web page is clear, accessibility tools like screen reader can do their best in serving such users.
What should I do?
The answer to this question is straight forward. The only way we can make proper web pages is by learning these elements carefully and use them as best as we can. Using the right elements for the right context is the only way to produce semantically correct web pages.