Broadband definitions continually change, but in 2017 the US definition of broadband is 25Mbps (megabytes per second) downstream and 3Mbps upstream. This is fast enough to stream music, movies, web surf, and read blurbs on innowiki.
Background
Early internet users used slow dial-up modems. The last mass-produced dial-up model ran at 56Kbps, about 1/450th the speed of broadband. In other words, a file that takes a minute to download on broadband took 450 minutes (7.5 hours) to download on the fastest dial-up modem.
Businesses, including the early independent internet service providers, connected via faster fiber-optic lines called T1’s and T3’s. T1’s carry data at 1.5Mbps and T3’s carry data at about 45 Mbps. T1’s were extremely expensive in the late 1980s and T3’s even more so.
One major problem with T1’s and T3’s is they require fiber-optic cables. The vast majority of homes lacked fiber-optic connections. A “last-mile problem” is the term for this lack of infrastructure. That is, figuring out how to economically bring high-speed internet from a close-by switching station the last mile to an individual house.
ADSL
Asymmetric Digital Subscriber Lines, ADSL, was an early enabler of broadband and remains a popular option in regions with copper phone lines but without cable television. Bell employee Joseph Lechleider invented DSL. However, the only mention about his invention is in his 2015 obituary.
Lechleider found that most users downloaded data, pulling information from the internet, much more than uploading. Therefore, data lines partitioned to prioritize downloading could be greatly increase perceived speed.
Cable Modems
Rouzbeh Yassini theorized data and television could co-exist on the same cable. Other engineers thought carrying television and data over the same line was impossible. He invented the cable modem and launched a company that was quickly acquired by Bay Networks for $59 million in 1996, as the Internet was becoming popular (at the time of the sale there were just 25,000 cable modems in use). Subsequently, he joined Bay Networks as an employee.
Especially in the US, cable modems became wildly popular. In 2010 there were about 73 million US cable broadband internet subscribers. Subsequently, in 2018, that number increased to about 100 million cable internet subscribers.