Jaiku is a competing (well not really) service to Twitter -- it's not nearly as popular, and that's the reason Google has decided to release it as an open source project for the community to develop.
JaikuEngine -- the new open source project --is different from Jaiku in a couple of ways, but for the most part it's identical.
JaikuEngine differs from Jaiku in a few key ways. Although core features like the website, SMS (in the US only) and IM bot still work, feed fetching and international SMS are no longer available. -- Jaikido Blog
JaikuEngine is likely the best open-source micro-blogging platform currently available, even though it's pretty much locked into using Google App Engine at the moment. I would love to see someone port this to a LAMP environment -- at that point, I'd expect adoption to be much higher.
Micro-blogging is becoming a very interesting space to watch over the next couple years -- will this move by Google put any pressure on Twitter? I guess only time will tell.