Although the majority of people use just the one web Browser, there are numerous others. Each one has it's own way of interpreting and thus displaying the data that makes up a website.
Usually the differences between the Browsers are subtle — the text may appear slightly larger in one browser or operating system compared to another. Other differences are more noticeable — a whole area of text may appear in a completely different part of the screen due to a rendering bug in the browser.
There are a set of guidelines for Browser Manufacturers to follow set up by The World Wide Web Consortium (W3C). If all the Browser manufacturers followed these guidelines then Web Designers wouldn't have to worry too much about testing their sites in multiple browsers and operating systems. Unfortunately some Browser Manufacturers decide to break the rules and neglet to make their Browser follow these guidelines, the most popular browser, Internet Explorer (IE) being probably the worst culprit. IE versions 9 and onwards are however a vast improvement on previous versions of Internet Explorer.
Some people are still stuck with using these early and slightly buggy versions of Internet Explorer, either due to a company running proprietary software that is not compatible with more modern browsers or because their operating system does not support more modern versions. For example, Windows XP which only runs Internet Explorer 8 and below, although other Browsers are also available for Windows XP such as Chrome and Firefox.
All the sites I create are tested for Compatibility on Internet Explorer 8+ (some older sites have fixes for IE 6 & 7), Firefox, Chrome, Safari and Opera on both Windows and Apple Mac Operating Systems.
Why not have a look at how well your chosen browser compares to others.