Google Buzz is integrated into the GMail web client, so you can check your regular google mail and see the Buzz at the same time.
Buzz is basically Twitter, with the emphasis on saying whatever you like (and including a photo or a link). This appears in your timeline, and also appears in the timeline of anybody following you. Yes, as with Twitter, you can follow people and you have followers. Your public timeline not only contains your own buzzes, but also contains buzzes of people you're following - unlike Twitter.
Whether Buzz takes off - and gets into the psyche of the public, not just the early adopters - really depends on who uses it. Will people stop using Twitter, or will Buzz mostly feed off Twitter's scraps from the few who integrate both services?