***     Bucket*** is the size of the area (square pixel dimensions, generally an integer power of 2, i.e., 4,8,16,32,64) which is calculated as one task.  This is why you see little squares slowly composite an image during a render.

     Each processing thread is assigned a bucket;  when it finishes, it is assigned another bucket.  If you have a multi-core processor, each core will run a thread;  if the processor is HyperThreaded, it can run a second thread for each core - so a HyperThreaded quad core like the core i7 will render in eight threads, which means working on eight buckets at a time.  That is why a core i7 will render much faster than a single core processor, even if both are running at the same clock speed.

     A larger bucket size is more time efficient if you have the RAM to support it.  How much memory is needed depends on render size, scene complexity, materials, and render quality settings.  If you are running short on RAM or if you want to see visible progress (finished buckets appearing on screen) more often, you can lower the bucket size.  If you see Poser decrease the bucket size during a render, you're running low on memory.  If Poser decreases the bucket once, then decreases it again, you probably won't get a finished render.

The system resource load goes up geometrically as you increase bucket size;  a bucket size "4" juggles 16 pixels, but a bucket set to "8" has 64 pixels.

 

edit:  Onnetz and Mark beat me to the post!  ^^

Poser 12, in feet.  

OSes:  Win7Prox64, Win7Ultx64

Silo Pro 2.5.6 64bit, Vue Infinite 2014.7, Genetica 4.0 Studio, UV Mapper Pro, UV Layout Pro, PhotoImpact X3, GIF Animator 5