Your 2007 MacBook has a Core 2 Duo intel CPU. It will run 64-bit applications.
4GB of physical RAM is NOT an issue for you, as your MacBook's Southbridge CPU to memory interface chip is lucky if it can handle 3GB of RAM (I think 2GB is the official max).
Your signature says you have Leopard (10.5) installed. If you have a 64-bit application, and it says it runs on Leopard, then it can run as a 64-bit app. You can use Applications -> Utilities -> Activity Monitor -> Kind to see if it is running as a 64-bit application (it will say 64bit if it is running as a 64-bit app).
Your 64-bit app can use more (lots more) than 4GB of "Virtual" memory (via paging and swapping to disk), but since your MacBook cannot hold 4GB of physical memory your app may not see much benefit from running a 64-bit app on your MacBook.
If you upgrade your MacBook to Snow Leopard (10.6), and look at Activity Monitor, you will see that many of the Mac OS X provided applications and daemons run as 64-bit applications (most of them do not need lots of memory, they just run as 64-bit apps because they can).
If you get a newer Mac which supports stuffing more than 4GB of physical memory inside, then any application which can run as a 64-bit app will be able to consume more than 4GB of physical RAM during its operation (assuming the app cares to use that much memory). The current MacBook Pros, the iMacs, Mac minis, and Mac Pros all support 8GB or more of memory. The MacBook line is limited to 4GB physical RAM in the current generation.
As for booting the Mac OS X kernel in 64-bit mode, most consumers do not need this feature. It is useful to developers writing new 64-bit drivers, customers that MUST install and run a specific 64-bit driver (very rare), or customers that need to squeeze every last ounce of performance out of their Mac and tests show the application they are using will do that.
The downside to booting the Mac OS X 64-bit kernel, is that not all developers have updated their drivers for 64-bits. If you depend on a specific 3rd party driver that has not been updated, then booting the Mac OS X 64-bit kernel will keep that driver from loading.