OK most people surfing the Internet use the most recent version of Microsoft's Internet Explorer indeed there are many people who do not even realise that there are alternatives let alone use them. But there are most are free.
Firefox is a browser which is popular with the more advanced web surfers, because of its features, many of which the latest version of Internet Explorer has "copied" to catch-up.
Google launched Chrome which is fast and highly likely to gain in popularity in the next few years.
Safari is for Mac users but can be used with a PC.
Whilst these last three are not so well known it is not uncommon for a website to display fine in Internet Explorer and not in the other three. This is because of how Microsoft until recently did not take a great deal of notice on the "rules" which set out how a website should display.
The consequence is that Microsoft's previous browsers allowed developers to "get away" with poor coding of websites, whilst the other three browsers did not.
The solution as far as a person specifying a website is concerned is ask for a website which will work in all 4 versions of the above browsers.
For a comprehensive web browser testing tool take a look at web browsing software tester.