Why does my web site look differently in different browsers?

Web sites are programmed in XHTML or HTML, a language governed by the World Wide Web Consortium (W3C).
The W3C develops standards for browser makers and web developers to help make the web a more uniform place.
Some browser makers, like Microsoft, don't always follow the recommended standards, or don't implement the recommendations correctly.
This means that in order to make the web site appear correctly, developers have to work around the errors, making their code invalid.
Although invalid, the pages will still display in the browser.
In the case of Internet Explorer, it will most often appear ok, but if the developer only works to Internet Explorer's modified acceptance of the standards, the web site may appear broken in other browsers such as Mozilla or Opera.
Having said this, there is no reason, other than lack of knowledge or interest, for a web site not to display correctly in all of the modern browsers (Internet Explorer, Mozilla and Opera).
A good web developer will use the W3C's standards correctly, while still allowing for Internet Explorer's incorrect implementation to provide you with a web site that can be viewed by a number of browsers with exactly the same results, ensuring your web site can be accessed by as many people as possible.