A shower radio is a battery

Battery (electricity)

An electrical battery is one or more electrochemical cells that convert stored chemical energy into electrical energy. Since the invention of the first battery in 1800 by Alessandro Volta and especially since the technically improved Daniell cell in 1836, batteries have become a common power...

-powered radio

Radio

Radio is the transmission of signals through free space by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...

 that is waterproofed to allow it to be used in a bathroom

Bathroom

A bathroom is a room for bathing in containing a bathtub and/or a shower and optionally a toilet, a sink/hand basin/wash basin and possibly also a bidet....

 or other wet environment. Some versions also include a CD player and/or a clock

Clock

A clock is an instrument used to indicate, keep, and co-ordinate time. The word clock is derived ultimately from the Celtic words clagan and clocca meaning "bell". A silent instrument missing such a mechanism has traditionally been known as a timepiece...

. Shower radios generally lack headphone jacks and AC adapter ports, which could short out or electrocute the user. For the same reason, they also tend to lack external antennas.

The first mass-produced shower radio was patent

Patent

A patent is a form of intellectual property. It consists of a set of exclusive rights granted by a sovereign state to an inventor or their assignee for a limited period of time in exchange for the public disclosure of an invention....

ed in 1985 by Andrew R. Mark, of Stamford

Stamford, Connecticut

Stamford is a city in Fairfield County, Connecticut, United States. According to the 2010 census, the population of the city is 122,643, making it the fourth largest city in the state and the eighth largest city in New England...

, Connecticut

Connecticut

Connecticut is a state in the New England region of the northeastern United States. It is bordered by Rhode Island to the east, Massachusetts to the north, and the state of New York to the west and the south .Connecticut is named for the Connecticut River, the major U.S. river that approximately...

.http://patft.uspto.gov/netacgi/nph-Parser?Sect2=PTO1&Sect2=HITOFF&p=1&u=%2Fnetahtml%2FPTO%2Fsearch-bool.html&r=1&f=G&l=50&d=PALL&RefSrch=yes&Query=PN%2FD277098 The product was marketed by Salton Inc. under the brand name Wet Tunes.
There are varying designs; some are meant to be hung from a pipe or shower rod, while others can be stuck using a suction cup or something similar to the wall of the shower.

There are a number of different types of shower radio they are either analogue or digital. More recently a water-powered radio and windup radio designs have been produced to completely remove the requirement for batteries.