Validation ensures correct parsing, not rendering
Many times I hear people say that their pages "validate, but still won’t display right". However, it is important to remember that validation only checks a page’s adherence to a particular document type declaration, and whether they are syntactically well-formed as a markup document.
Validators don’t somehow also magically determine whether the page is actually constructed to display an aesthetically pleasing image, or the "correct" one that the developer expects to appear, and they definitely can’t tell how well a HTML document will display across various browsers. That is something that developers have to figure out themselves.
Nevertheless, if a page is invalid, then it is impossible to say how a certain user agent will interpret the content, and multiple quirks are likely to appear as the parser attempts to make sense of your technically mangled code – and by then, it’s not very easy to proceed to creating a correctly-rendered page, either. So validation does matter when you are creating markup documents, but it is entirely possible to create perfectly valid documents that still look really strange when actually rendered.