It’s nothing to do with HTML…it’s related, primarily, to CSS.
Cross browsing (although I think you mean cross browser) means that what works in one browser will work in another (or all).
As new features are evolved for CSS such as border-radius or gradients we have to come up with ways (if it’s a requirement) to try and achieve the same effect across multiple browsers.
Sometimes that’s a matter of just a vendor-prefix, sometimes it’s a fallback property or a javascript method.
And sometimes we just don’t bother at all.