They have a cache, they are not actually searching the whole internet every time you ask something. They have scripts (call robots IIRC) that crawl from link to link and take notes. Sometimes the site changes but the robot hasnt seen those changes yet, so google does not know about that yet.
Right of the URL there is a little triangle, klick on that to get the cached version.
I've seen that many people and companies are now asking to be removed from google in europe. I do not like this development, as it makes way for censoring. Who's to decide what's to be removed or not? If a banker makes wrong calls, should his track record be cleaned out? What about someone being deliberately smeared online, should the smearing be cleaned out? And who's to decide which rules shall apply and, who's to enforce the rules, and will the rules be enforced justly?
As for google, they do retain caches for a while, i do not know for how long, but there are also other sites, like the internet archive and maybe others (?) do store snapshots of pages from time to time, so if you see someone removed something online, you can often go there and get it.
