The 8051 architecture has three separate address spaces, the core RAM uses an 8 bit address, so can be up to 256 bytes, XDATA is a 16bit address space (64Kbytes) with read/write capability, and the program space is a 16bit address space with execution and read-only data capability. Because of its small address range and close coupling to the core, addressing the core RAM is more efficient in terms of code space and access cycles
The original 8051 core had tiny-on-chip RAM (an address space of 256 bytes but some variants had half that in actual memory), and XDATA referred to off-chip data memory (as opposed to program memory). However most modern 8051 architecture devices have on-chip XDATA and program memory.
So you might use the core memory when performance is critical and XDATA for larger memory objects. However the compiler should in most cases make this decision for you (check your compilr's manual, it will describe in detail how memory is allocated). The instruction set makes it efficient to implement the stack in core memory, whereas static and dynamically allocated data would usually be more sensibly allocated in XDATA. If the compiler has an XDATA keyword, then it will override the compiler's strategy, and should only be used when the compiler's strategy somehow fails since it will reduce the portability of the code.
[edit] Note also that the core memory includes a 32byte bit-addressable region, the bit-addressing instructions use an 8bit address into this region to access individual bits directly. The region exists within the 256byte byte addressable core memory, so is both bit and byte addressable[/edit]