It was the way you knew friends were available to chat. It was much closer to in-person conversation than most media we use nowadays.
It's not uncommon for someone to {iMessage, SMS, FB Message, IG Message, etc.} me while I'm otherwise busy. Then, I need to find a second to let them know of this (unless I either totally drop the ball or consciously decide to not reply). I also need to let them know I'll be free to chat after work, at lunch time, etc.
With AIM, you just logged in and set whether you were available, idle, away, or invisible. Friends knew whether they would disturb you or not.
Not only that but it was pretty much the singular form of instant communication that almost everybody used. Now I have people I reply to on multiple platforms such that we'll even branch off in separate conversations per platform, I only talk to on X, Y, or Z platform, etc.
I'm not one to <Old man yells at cloud> typically but this is one aspect of social media that I think we've lost over the past decade and it really sucks.