Welcome to Android Central!
Touchwiz is the name of Samsung's custom spin of Android, which includes (among other things) a unique visual style on the homescreen, some additional widgets (like a widget with current time and weather conditions), their own versions of email and calendar apps, and a re-arrangement of the settings menu. You don't really use Touchwiz the way you use other apps - you use it automatically just by using the phone.
And the more recent versions are called Samsung Experience.
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