The name, cupsole, is abit of a 'giveaway' of how it is designed and configured. The cupsole is designed like a cup: with high sided 'walls' and a hollow centre.
A cupsole enables EVA foam, or other cushioning insoles, to be placed inside and glued onto the 'floor' of the cupsole. The upper of a cupsole shoe is placed inside of the 'walls' of a cupsole, and the upper and cupsole are then stitched together. The giveaway 'sign' that a shoe is a cupsole shoe is the line of stitching that runs around the shoe's midsole; as shown on the top image. There are two primary types of sportswear shoes: those using a cupsole and those with a vulcanised sole. The majority of Adidas shoes have historically featured a cupsole: due to the stitching of the cupsole/upper providing extra strength and durability, and it's design providing more 'scope' for midsole cushioning.
However, Adidas began designing and manufacturing skateboard shoes in the 2000's, and due to vulcanised sole's being favoured by skateboarders, there are more Adidas shoes with a vulcanised sole. Vulcanised sole's use glue and foxing tape to attach the sole to the upper. This means that a vulcanised sole rarely has midsole cushioning, and the shoe provides more 'feel' and feedback to a skateboarder. In conclusion, the primary advantage of a cupsole is that it provides extra cushioning protection, but, with the drawback of providing less 'feel' due to the extra layers placed between the foot and the floor.