What blurring is good for
The most common use is a background. A blurred photograph behind text stays interesting without competing for attention, because the eye has no sharp detail to settle on. The same trick makes a convincing placeholder while a full image loads.
Blurring also hides information — a house number, a face in the background, a name on a document. Bear in mind that a light blur can sometimes be reversed on text; for anything sensitive use a heavy radius, and check the result before sharing.