The portable telephone was another "must have" technology in the 1980s. When these phones came on the market, everyone had to buy one. Maybe it was cell phone envy? Who knows.
When they first came out, these phones were incredibly simple. The handset was, essentially, two walkie-talkies in a case. One walkie-talkie handled your voice, while the other handled the voice of the caller. That way you did not need the push-to-talk button of a normal walkie-talkie. Theses phones used the standard 27 MHz and 49MHz frequencies that walkie-talkies and baby monitors use. That meant short distances and a fair amount of interference, along with the fact that your neighbors could listen in on your calls.
Even so, cordless phones were popular because you could get rid of the cord and walk around the house or yard while talking on the phone.
The reason these phones exploded in popularity, by the way, is not because of the technology. Walkie-talkies had been around for decades. As with the answering machine, the explosion came from the breakup of AT&T and the deregulation of what you could connect to a phone line.
See How Cordless Telephones Work for more details.