The parsing rule of HTML5, which analyzes the meaning of mark-up, has been more precisely defined in HTML5. Until the introduction of HTML5, only the meaning of valid mark-up was defined, meaning that as soon as one small error was made in the mark-up (most Web sites have at least one), the behavior was undefined. Essentially, it meant that all browsers behaved differently, which is no longer the case. Now, faced with errors in the mark-up, all compliant browsers must behave exactly in the same way.
This requirement helps Web developers quite a bit. While it is true that all modern browsers now use these HTML5 parsing rules, non-HTML5-compliant browsers are still used by some. Keep in mind that it's still highly recommended that one write valid mark-up, as such code is easier to read and maintain, and it greatly decreases the prominence of incompatibilities that exists in various older browsers.
Don't worry — you don't have to change anything on your Web site — the Web browsers' developers have done everything for you!