Where's the fun in having a computer disconnected from other computers, isolated in the world, just a solitary machine and not being able to share what we like with others? A hint: there's no fun. So, if it wasn't for the internet the computers would have been an one person pastime even today.
But in 1965 everything changed when two computers established a communication for the first time, using a technology called packet switching. This technology breaks data into small packages making its traffic easier and distributing them into a web of connections instead of using a direct path.
The original papers of Lawrence Roberts, one of the main scientists behind the packet switching project, are available on his personal website.