Do these sunglasses actually block UV?

The lenses are stated as UV400, which blocks 100% of UVA and UVB. That is the same protection rating used on many sport and fashion sunglasses.

What does shatterproof mean here?

The lenses are described as shatterproof, so they resist breaking into sharp pieces on impact. That makes them a safer pick for beach and party use than standard glass lenses.

Are these good for running or cycling?

They are aimed at the beach, parties and holidays. The rimless front gives little side coverage, so they suit casual wear better than fast sport where wind and glare come from the sides.

The listing describes the sunglasses themselves. A case or cloth is not stated, so plan to store them in something soft to protect the mirrored lenses.

How do they compare with framed mirrored sunglasses?

They share the mirrored UV400 lens but drop the frame around the lens. That makes them lighter and sleeker, with less protection at the edges than a wrapped or full-frame pair.