Lots of wrong or half-wrong information here, let me try if I can set this straight. I'll try to make it not overly technical (at the expense of some accuracy, but please bear with me):
1. There's an important difference between available memory and address space. Available memory is the total size of RAM in your machine (usually about 2-8 Gigabyte), plus your "virtual memory" - that's hard drive space set aside for Windows to use as swap space when there's not enough RAM. You can envision your computer like a huge cloakroom, in which clothes are constantly stored and retrieved. Your RAM is the main cloakroom, it provides quick access. Your virtual memory is an additional storage space behind the main cloakroom - it offers additional space, but it takes longer to access. For Civ4, modern computers usually have enough memory, though I'd recommend to have 3 GB of physical RAM (= main cloakroom space) for super-huge games, otherwise you may have long waiting times while the game swaps data around between physical and virtual memory.
2. Address space is, in our cloakroom analogy, the range of retrievement numbers that can be given out to customers. This is NOT related to the actual capacity of the cloakroom, it's just a fixed amount of "number slips" that are printed for every cloakroom. This leads to two possible problems:
Problem 1: There may be more number slips than there's actual cloakroom capacity, so someone may want to store a cloak, and there are still numbers that could be given out, but there#s simply no capacity left to store the cloak. In this case the cloakroom will stop to operate (in PC terms: If Civ4 tries to allocate more memory than the total memory of your machine, then it will crash).
Problem 2: The number slips may run out although there's still room in the cloakroom, so someone may want to store a cloak, but can't, because there's no number slip that he could be given, even though there's still a lot of free space in the cloakroom. In this case, the customer will not be able to store his cloak (in PC terms: If Civ4 tries to allocate more address space than your operating system provides, then it can't store any more data and will most likely crash).
3. You can envision a 32-bit Windows as having about 4 billion number slips that can be given out. However, half of those are reserved for cloakroom employees (i.e. Windows' own processes, which require memory and address space as well). So a single customer (Civ4) can at maximum have access to 2 billion slips, and store 2 billion cloaks - even if the cloakroom has room for much more.
4. However, there's a special rule in our cloakroom: Every customer always wants to store hundreds, thousands, or even millions of cloaks at once, and each set of cloaks must be given a contiguous set of numbers. So, if the customer wants to store 1 million cloaks, then the cloakroom needs 1 million of contiguous number slips, with not a single one being already occupied or missing, to hand out to him. This leads to a third possible problem:
Problem 3: Even if there is enough space in the cloakroom, and the wardroom has enough number slips left, there may not be enough _contiguous_ number slips for a given set of cloaks. Let's say the customer wants to store 1000 cloaks, and we have 1200 number slips left, more than enough. But if these number slips have e.g. the numbers 301-900, and 1201-1800, then the set of cloaks cannot be stored.
5. Also, the customer will keep _all_ number slips of a given set of cloaks until _each_ of these cloaks has been retrieved. Therefore, there may be number slips that currently aren't actually used to store any cloaks, but which can't be given out for new cloaks, because the customer hasn't returned them yet.
This is the reason why it's important to understand the difference between memory (cloakroom capacity) and address space (number slips available). Even if Civ4 currently only occupies, say, only 1.6 GB of memory, it may be allocating 1.95 GB of address space already. Unfortunately, when you check Civ4's memory usage in the task manager, it will only tell you the actual memory usage (the number of cloaks Civ4 has actually physically stored in the cloakroom). Civ4 may have nearly exhausted its available address space (about 2 billion numbers) already, you just don't know - at least not from the display of the regular task manager. Hence, if Civ4 crashes while occupying 1.6 GB of memory, then the reason for the crash may be that it exhausted its 2 GB of available address space.
6. Because many programs required more than 2 Gb of address space, there's a setting that tells Windows to enlarge the address space to 3 GB. This setting is activated by booting Windows with a special command, the "3GB switch". Note that there are still only 4 GB of address space in total, it's just divided differently: Previously, it was split in half between Windows and Civ4. With the 3GB option switched on, Civ4 gets 3 GB of address space, while Windows will have to make do with 1 GB. In our cloakroom analogy, this means that 1 billion number slips that previously were reserved for cloakroom employees, can now be used by the customer.
7. Of course, this only works if the customer actually understands numbers bigger than 2 billion. In PC terms, this is signified by a "flag" that can be set (or not) inside each program. For Civ4 BtS 3.19, this flag is already set. This means, the program _can_ handle numbers bigger than 2 billion. Of course, this flag is only effective if used together with the 3GB switch mentioned above, which causes Windows to actually allow Civ4 to access addresses in this range.
8. In a 64-bit operating system, the address space is much, much larger than 4 GB. (It's like a new form of cloakroom which has many more number slips than the previous versions.) However, the customer still needs to understand the numbers given to him. In PC terms: A 32-bit program that has doesn't have the "flag" enabled, will still only underatnd numbers up to 2 billion. Civ4, which has the flag enabled, will understand numbers up to 4 billion. A native 64-bit program will understand numbers much, much larger, but Civ4 is a 32 bit program, so 4 billion is the limit.
Hrm. Still quite a wall of text. But I hope it helps to understand why there are different types of memory limitations, and what the mysterios 2 GB barrier, 3 GB switch, flag, and 32-bit vs 64-bit addressing, mean in terms of Civ4's playability and stability.