What program ?
programs can also not be patch to 64-bit its entirely different code therefore a fresh install is required.
64-bit computing allows programs and operating systems to access more than 4GB of RAM which can be useful for demanding applications such as games, photoshop rendering etc. However this is not related to CPU cores that is something different. This depends on how the program was written so it can take advantage of multiple threads (CPU cores - real and virtual). Many programs/applications are now multi-threaded and utilize 2-8 cores normally (more is possible but for consumer grade stuff thats the range usually). Handbrake (encoding program) can use all 8 of my threads on my i7 920 which allows the encoding process to be dramatically decrease in time compared to single or dual cores. However many olders games i have only use 1 thread and ignore the other 7.
Hope that helps