According to the description on the Opera 12 alpha download page, it uses 30% less memory on Javascript, 40% faster load time for secure websites, supports 3D content, and Hardware Acceleration from your videocard/GPU.
I been using Opera 12 Alpha for a few hours, and it is pretty fast.
I think having 3D in the browser mean you can play 3D games without the need to install them on your PC. You can just open up your web browser, and go to a website with 3D games to play games. I bet this might lead to some people illegally making browser versions of some 3D PC games via ROMs, and hacks to let people play for free with emulators on a website.
No, only when playing 3D games. If the website is in 2D, the 3D part will be turned off. Plus, if you have a medium to very fast video card, you probably won't notice any lag at all.
I believe, Firefox 4-6, Chrome, and even Internet Explorer 9 supports 3D on websites.