OS X has supported 64-bit executables since 10.5 Leopard (or 10.4 Tiger for command line applications), and has had a 64-bit kernel since 10.6 Snow Leopard.
The main advantage of 64-bit (in this context) is that applications can address more than 4GB of memory. When working on large amounts of data this allows faster processing, as there's less need to swap data in and out of memory.
But 32-bit applications still work, even where a 64-bit operating system is running on a 64-bit Mac, so there wasn't much pressure on developers to create 64-bit versions of applications that weren't routinely used with large amounts of data.
But that's about to change.
Microsoft this week made a 64-bit version of Office 2016 for Mac available via the Insider Fast channel. (The Office Insider program provides a way for users to access the latest product builds, so it's essentially a beta program.)
According to the announcement, "we've been hearing from customers... that 64-bit versions of Mac Office are desirable to enable larger address spaces, better performance, and new innovative features" and so "we're currently preparing to release the Office apps in full 64-bit".
The main problem with 32 to 64 migration occurs when an application uses plug-ins/add-ins. In general, those items need to match the application and so users can't mix 32-bit add-ins with 64-bit applications.
Microsoft is encouraging add-in developers to prepare for the general availability of the 64-bit version of Office for Mac.