Why is valid html so important and why should you care about it?
In order for search engines like Google to show your website in its search results, Google must spider or crawl your website first, save a copy of it (well, the first 100k of the page at least), and parse its contents so it can better understand what is important.
If the spidering engine encounters too many error or issues, it will be discarded. Also, errors can also cause your website to display improperly, of course.
There are many things to remember in web design when it comes to proper and valid html. Proper tag usage, the order of the tags, and ensuring that items are where the search engine(s) expect to find them. For example, cleaning up the head of your document(s), proper language indicators, valid microdata or JSON, and the appropriate attributes for assets like images. Add to this, accessibility settings for the sight or hearing impaired.
There are many free tools on the internet for checking valid html on webpages and you really owe it to yourself to utilize them. It may take a little time and patience, but you will be well rewarded with higher search engine rankings.