Back in the day, the bulk of Internet users were on university networks, and they gave everyone access to Unix systems where anything you put in public_html goes up on the university's website under your username.

For example, I went to UTD from 2003 to 2007. This was long after the days of "the bulk of Internet users were on university networks" were over, but the infrastructure was still there. All students had ssh access to a handful of machines, the main one being apache.utdallas.edu.

So I could do this:

    $ scp picture.jpg ajb0##[email protected]:./public_html

And then anyone would be able to access it at:

    http://www.utdallas.edu/~ajb0##000/picture.jpg

(FYI, at UTD, everyone's username was their initials followed by a six-digit number where usually only the second and third were nonzero... I ##'d that part out because I don't feel like giving out the exact username I had back then... especially since my initials were different)

Edit: And even if you weren't at a university, back in the dialup days it used to be that even with home internet, everyone's computer was directly on the Internet with no NAT or any kind of firewall, so you could just install Apache on your box and serve what you wanted. On paper, most ISPs banned that practice in their TOS, but it was never enforced. The real impediments were that a) dialup connections would usually disconnect if you went idle too long and b) most people had dynamic IP addresses that changed every time you dialed in (for the latter, DynDNS was a godsend). And of course dialup bandwidth was shit, so hosting anything substantial (especially an image!) would slow down your connection (seriously, people would actually buy second phone lines from their telcos and maybe even get a second account with their ISP so as not to tie up their main connection).

Broadband made it easier: even with a NAT router, you could just forward port 80 to your desktop, and you won't have to worry about bandwidth, your connection would stay up 24/7, and even if your IP was technically considered dynamic it would almost never change. What really sunk the concept of hosting your own was a) mobile (good luck running Apache on your phone, and getting port forwarding on a mobile network is impossible) and b) the rise of services like Imgur that let you host shit with no hassle (Facebook killed self-hosted personal home pages for the same reason).