As far as I know, there are more than eight Daoist immortals so I’m not sure what sets the eight, in the group known as The Eight Immortals (Bāxiān 八仙), apart from the rest.
Each immortal has an instrument or implement onto which the immortals may transfer his/her power. These instruments are known as the Covert Eight Immortals (暗八仙).
The exact identities of the Eight Immortals are unknown, but some of them are associated with actual historical figures born during the Tang and Song dynasties. Apparently they reside on a group of five mythical islands in the Bohai Sea, namely Mount Penglai (蓬莱) Island, Fāngzhàng (方丈), Yíngzhōu (瀛州), Dàiyú (岱輿), and Yuánjiāo (員嬌).
Here is a picture of the eight on a Chinese postage stamp. The painting depicts them crossing the sea and refers to a famous story about them travelling to a banquet hosted by the Queen Mother of the West. The eight must cross an ocean to get keep their appointment and they decide on a friendly competition, each one using their magic instrument to make the crossing.
The Eight Immortals crossing the sea, each showing their special talents (八仙过海，各显神通) is the Chinese saying that has arisen out of this story. Read metaphorically, it means that every person will tackle a problem or carry out a task using his/her own unique talents and strengths.
I shall write about each of the immortals in separate posts.