HTML specifications such as HTML5 define a set of rules that a document must adhere to in order to be “valid” according to that specification. In addition, a specification provides instructions on how a browser must interpret and render such a document.
A browser is said to “support” a specification if it handles valid documents according to the rules of the specification. As yet, no browser supports all aspects of the HTML5 specification (although all the major browser support most of it), and as a result, it is necessary for the developer to confirm whether the aspect they are making use of will be supported by all the browsers on which they hope to display their content. This is why cross-browser support continues to be a headache for developers, despite the improved specifications.
HTML5 defines some rules to follow for an invalid HTML5 document (i.e., one that contains syntactical errors). However, invalid documents may contain anything, so it's impossible for the specification to handle all possibilities comprehensively. Thus, many decisions about how to handle malformed documents are left up to the browser.
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