In 1965, Gordon Moore noticed that the number of transistors on integrated circuits was doubling about every 2 years. This means that computers’ processing power was also doubling roughly every 2 years (sometimes this is quoted as 18 months due to the combination of the numbers and speed increasing). Moore said that he expected this trend to continue for at least 10 years.
Believe it or not, Moore’s law didn’t just last for 10 years, but was still accurate 50 years later (it has slowed down a little since 2015). This means that computers today are over tens of million times faster than in 1965! Moore’s law also applies to other improvements in digital devices, such as processing power in cellphones and the number of pixels in digital cameras.
The exact numbers will depend on what is being described, but the main point is that the processing power is increasing exponentially – exponential growth doesn't mean just getting a lot faster, but getting unbelievably faster; nothing in human history has ever grown this quickly! To illustrate this in reverse, the time taken to open an app on a smartphone might be half a second today, but a 1965 smartphone would have taken over a year to open the same app (and the phone would probably have been the size of a football field). It's no wonder that smartphones weren't popular in the 1960s.