In the twenty first century, the word "wireless" is often associated with the computers, the internet and mobile phones. A connection is established without any wires - hence, wireless. It is typically referred to as "wi-fi." Put very simply, wi-fi uses electromagnetic or radio waves to create a connection which allows people from all over the world to connect and interact with each other. It also ensures that remote areas can have some access to technology although connectivity may be unreliable. Communication is enhanced and relationships are formed without the need for expensive and endless travel. This also creates business opportunities which may otherwise not exist.
In the early nineteenth century, the connection between electricity and magnetism was widely explored, and eventually, in the early twentieth century, the "radio" became the means through which many people were able to listen to broadcasts of information or even for entertainment, long before the invention of television. Due to the fact that radios operated wirelessly, they were often referred to, interchangeably as either radios or wirelesses (especially in the U.K.) The term wireless to mean radio was used extensively until about the 1960s and 1970s. With the introduction of other wireless technologies, the word wireless to mean radio eventually became obselete.
Accordingly, the question "Why was there a wireless in the church?" is using the outdated meaning for radio and is asking why there was a radio there and what its purpose was.