The article of clothing is called a bolero, usually referred to in the US as a cropped shrug. They're an informal version of the bolero jacket, a very old and very European article of clothing that both men and women have worn in the past seven centuries or so.
Bolero are seen quite often with formal dresses to help them seem modest or prim, and tailored ones can make an otherwise inappropriate top slide by office dress code. This is pretty much what they were used for in the far past. They would be paired with a strapless dress to hide the skin on the arms and shoulders.
I like thin crocheted bolero, and lace ones can be really sexy. Strapless top, pushup bra, sheer lace covering the shoudlers and arms...it's a powerful arguement. In the winter, they can be useful since they will literally fit in a purpse pocket and provide some degree of protection against the cold for the arms.

I'm done defending myself now!