A browser is simply a computer program that displays websites. If it helps, think of your browser like a TV and websites like TV channels.
Just like any TV can watch the same shows, every browser accesses the same Internet. However, like TVs, different browsers can have features that set them apart.
The default browser in Windows is Internet Explorer, while Apple's OS X uses Safari. These come preinstalled on computers. The latest versions of these browsers are both stable and secure for most situations.
However, there are third-party browsers as well. Some users prefer these because they're faster, more secure or have cool features.