As several others have said, the primary benefit of a 64-bit DF is that it will directly permit larger worlds. Several versions back there was one that slammed against the 2 GB (Windows) barrier hard, and Toady had to re-optimize to fit things in a more space-efficient manner. But there's only so much diminishing returns you can get from such things; and in some cases optimizing for space can result in slower execution times.
Slightly less directly, I suspect that the "world coming alive", with complex diplomacy and in particular trade, will eventually require more information kept track of than will be practical for a 32-bit application to keep in its very limited RAM. The forward evolution of DF keeps track of more things as it adds features, and more things equates generally to more memory footprint. There will probably come a day when users with 32-bit OSs and/or with 4 GB or less RAM will only be able to run smaller and/or simplified worlds; perhaps not "soon", but eventually.
There are some possible tertiary benefits; much of the attention in modern CPUs and compilers is on the 64-bit side, so in the long run better tools help with a better product. There may be cases where speed increases can be had by throwing memory at optimization problems, and so on.
Hopefully, at some future point DF will become usefully multi-threaded; if for no other reason that *eventually* that will become something that compilers can do more or less on their own. At that point, one starts to be concerned about memory per core and not just the overall total; and it's much easier to keep track of when you have a large address space.