Does that mean nobody else can purchase a domain name say with the name apple and begin trading in the computer services industry???
Basically yes (it depends exactly what the apple trademark covers). However, you may be able to use it for a totally different industry/trade, like say heavy machinery, or maybe fruits. Why would you choose do that instead of coming up with your own unique trademark, is another question.
"apple" is in a way a special case, because it is a word, so there may be reasonable other uses for it. That's not the case for other terms though, such as say Google.
However, domain law is a bit hazey to be honest..
This is all about trademarks law. The domains and their usage simply have to comply with existing laws.
Of course, if one actually plans to choose the path of using an already registered trademark, one should get the advice of a lawyer specializing in this sort of stuff.
can be a good read.