Markup validation sounds like a technical topic, but it is a factor that must be understood so that your website will be available to the largest number of customers or readers.
Markup validation is the process that is used to make sure the code on you web pages conforms to the "rules of grammar" of the world wide web. If your pages are valid, not only can the most people access your pages now, but people will continue to be able to access your pages in the future.
You may well ask why having valid web pages is important. After all, if you are able to view your web page, and it looks nice, that's good enough, right? Well, not everyone has the same monitor resolution as you. What if someone wants to quickly buy your product, and all they have available is a cell phone? Having valid pages means that you present the data on your site in a certain predictable and agreed upon way. This means that the greatest number of devices, and so customers, will be able to access your site, since the makers of these devices will be able to count on the manner in which you give them information.
Additionally, as you've noticed, things change quickly on the web. If your site looks good today, unless it is valid, it may not look good tomorrow.... even on your computer. When the way we communicate over the world wide web is changed, attention is paid to making things backward compliant. In other words, many of the functions on old sites will still work with the new browsers and devices, as long as they worked with the old standards.
Essentially, designing your site without paying attention to being valid is like gambling. You gamble whether people on other computers and devices will be able to properly access your site, and you gamble whether people will be able to properly access your site in the future. Well, to narrow it down further, it's like playing Russian Roulette. If people can't access your site, they won't visit it. If people don't visit your site, they won't buy your products. It's not something you want to gamble on.
How can you tell, whether a page on a site valid? Fortunately that's easy. Just enter it's URL into a markup validator, like this one. You generally will not need to use a validator yourself, since your web designer will make the pages of your site valid, but it is nice to know that if you are curious, you can quickly tell whether your customers are likely able to access your site.
Here is some more information on markup validation. It is an explanation by the W3C, the organization in charge of the protocols and guidelines for the world wide web, as to why markup validation is important.