Well, one thing is when we're talking about 64bits system, actually we are talking about 2 separate things: 64-bit hardware support and 64-bit OS support.
In my understanding, if you can see 4GB or more memory in your system profile, then you have a 64-bit computer. (Whatever OS you use, there should be some system utils can help you to monitor the system status in runtime, e.g., system monitor for mac/u*x/, task manager for Windowz, etc.)
You may not really feel how 64-bit benefits you. But at least it's compatible with most of your current applications so you don't need to pay extra money to get the 64-bit edition for them.
Want to know more about 64-bit? Take a few minutes to read the following links:
- What kind of performance increase can I expect in going from 32-bit to 64-bit Stata?
- First Look: Leopard first looks: 64-bit support
- Is Leopard truly 64-bit?