This gif, animated by an artist who went by "Dead Karl", could be seen all over in my early days online. It was often reposted to Gaia Online forum signatures and whatnot, shared around by people because of its impressive quality and fun story. This was in a time before YouTube, and before we really watched that many videos online in the browser. You usually had to download videos to watch them, and gifs usually didn't present entire scenes and stories. (There were videos and stories told through Flash, though.)
For those who are younger, it might be interesting to note that part of the reason this could be shared around so much was because it was in 100% black and white (not even any inbetween shades of grey) as well as very tiny resolution-wise. At that time, the file size of images really mattered, and gifs could easily become too large to use due to colour range, amount of frames, and resolution. (We still see some of that today, but it was much more limited then.)
I didn't know anything about Dead Karl themselves. Judging by the language in the gifs, they seem to be Chinese. I was now able to find a link to a defunct website, which can be visited on the Wayback Machine: http://www.deadkarl.net/. They supposedly also had a site at http://www.rocktang.cn/karl/ , but I guess this hasn't been archived. Some of the famous gifs have been archived here at the Internet Archive.
(Image from: http://web1.nazca.co.jp/hp/suttoko/)
Dead Karl, and many others like myself, used a simple black and white raster animation program called EasyToon Setagaya Branch (the latter part refers to the version of the program). I had already made animations before that by drawing in MS Paint and putting the frames together in Windows Movie Maker, or by making animated gifs from image sequences using ImageMagick. But this was the first time I was able to use a real animation program where you could export directly as gifs and where you could use the "onion skin" function to see the surrounding frames for reference while drawing. I went on to self-study a lot of animation through books, "behind the scenes" videos of animated movies, and YouTube tutorials and documentaries from then on.
Here is one of my own EasyToon animations from ~2005. (The filename tells me that this is Hinata from Naruto.)
When oldschool forums were still popularly used, most of them had the option to show a "signature" at the bottom of your posts. You would edit it from your profile settings the same way you could change your icon or username or whatnot, and your signature would automatically attach to every post you made.
It could be used to link to your website, or to a page where you sold art commissions, or anything else you wanted people who came across your posts to see. Often it might also just feature your favourite quote, a cool picture, or a funny joke. And a specific genre of graphics developed around this - people making edited images for their cool signatures. There were also people who offered to make them for other forum users.
On some forums, like Gaia Online, it was common to see people have art of their characters in their signatures (whether commissioned, gifts, or their own art). You would also see adoptable pets in signatures, especially the hatchable ones that needed a certain amount of clicks or views to evolve (like Dragon Cave).
MSN Messenger was the main direct chat program we used when broadband access became common to the public here. Before that, we had the expensive and slow dial-up connection (if you had any Internet access at all), where you had to pay per minute and you couldn't use the phone landline at the same time. My family was relatively poor but my parents worked in tech, so we did have a computer and a dial-up modem, and I was allowed to go online for a short while here and there before we got broadband. During that time, I only used e-mail to directly write people rather than any chat programs, since the time most of us were able to be online was so limited, it was more convenient to send an e-mail and then check for a reply the next time you got on. However, right before we switched to MSN, I remember sending off so many e-mails back and forth between me and my friend that we were basically treating Outlook Express as a chat program, just replying to each others' e-mails within seconds of them arriving. (Outlook Express was the e-mail software we used - you could connect any e-mail to it and read your mail from the program rather than logging on somewhere in your browser.) I had a unique e-mail address based on our family website URL that we got for free from the provider, it was a long and confusing URL with a collection of random numbers and letters.
I was 13-14