Before dial telephones, we made phone calls through an operator. You picked up the phone, there was no dial tone, and you talked to an operator who placed the call for you. This was the only way to initiate a call; if the operator wasn't there, or was busy, tough luck. You didn't have any way to "dial" a number because you didn't have a dial on your phone.
The dial telephone was introduced in 1919 in the US, and spread until it was nearly universal in the 1950s. The dial tone, coupled with phones featuring rotary number dials, allowed callers to dial phone numbers themselves. It was a really handy system to deal with the growing number of telephones and telephone calls. In the 1960s touch-tone phones (those with buttons) began to take over from the rotary dial models.
But some towns held out long past the near-universal dial telephone system. If the call volume was low enough, or the city remote enough, it just didn't make economic sense to replace a working operator system with an expensive dial system. In this 1978 film from the AT&T Archives called "Good-Bye, Central," we see the last few cities in the United States that operated without dial telephone services. It's fascinating to see operators working the central switchboard in the late '70s. Looks like a repetitive, thankless job to me. Settle in and enjoy the tale of how telephones used to be:
If you liked that, check out this 1978 newspaper article entitled "Dial phones reach island," confirming in print that the 1,800 residents of Santa Catalina Island got dial service. You may also enjoy the '70s-riffic Simmons mattress ad to the right of the newspaper story.
Note: the dial tone and rotary dial telephone are two sounds your kids probably haven't heard.