blur circle.

Can someone explain to me how people are able to make blur circles?? I've seen them on sites like Pintrest and Instagram but I just don't get how they make them. They usually have like a gradient effect with some letters on it.

It's possible to blur the edges of a vector circle shape or any other shape by using the Feather parameter under the Mask tab in Properties if that's what you mean?
http://ezbackgrounds.com/blog/layer-mask...window.php