I stil don't really know what Twitter's purpose in life is.
It has 2 main uses:
1) Knowledge Gathering: Much like an RSS feed, you follow sources of news interesting to you. I follow local traffic reporters and radio stations and I get updates on local issues that let me know if I should avoid certain roads. This information is available elsewhere, but by using Twitter I filter it down to the stuff they think is most important. I also follow local 'regular' people so that when there's a big traffic problem (or just something fun going on) I'm likely to hear about it before the news even reports it.
2) A Friend Spam-Reducer: I follow several friends and family members. Often I'll want to invite people to things over the course of a week, but I have no idea who is interested. If I were to e-mail my entire address book that I was going to the movies tomorrow and the mall the next day, they would get annoyed with me for constantly spamming their e-mail inbox. But if I say the same things on Twitter, people who want to do something can check it out and folks who are busy can ignore it.
Twitter is like e-mail you don't have to check.
All those dumb links you want to send your friends? They'll get annoyed with you if you actually e-mail them all day. So I put it on Twitter and the people who are in the mood for that stuff today take a look.
Example: I often report on the status of my 2-year old:
http://twitter.com/JeffCarpenter/status/2880777057
http://twitter.com/JeffCarpenter/status/1363668120
http://twitter.com/JeffCarpenter/status/1561726209
My mother and grandmother often respond that they love seeing these things because when they want to check in, they can. But if I e-mailed them 6 times a day, they'd likely get fed up with that.
So it's a way to share without being an intrusive jerk.
The difference from Facebook and Myspace is that those require you to maintain pages with info and photos that you have to maintain. Twitter is much, much easier than that which is why it's more popular with adults than kids. It doesn't require all that overhead and extra work. A kid will take the time to make a myspace page. An adult just wants to follow CNN and be done with it.
I define Twitter as 2 things:
I wanted to e-mail you this, but didn't want to bother you if you're busy.
and
I want to read the most important part of 20 news sources this morning.