Why one page table per process

A page table usually has a fixed number of entries and therefore describes only a portion of the entire virtual address space. This is why you need multiple of them to cover the entire address space. Now, in many OSes processes have individual (in other words, not shared with others) virtual address spaces, which helps to protect processes from one another. This is another reason for having multiple page tables.

Page table translates from virtual to physical page addresses. Since each process has its own virtual address space and usually maps the same virtual address to a different physical address it needs a separate page table. Curiously, multiple processes may map different virtual addresses to the same physical memory. This can be used to implement shared libraries or inter-process communication.