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16 bit compilers compile the program into 16-bit machine code that will run on a computer with a 16-bit processor.

8bit compilers target microprocessors with 8 bit registers, same for 16 bit and 32 bit, and also 64 bit. Depending on the microprocessor each often has there on addressing scheme also for memory and hardware.

for each of 8/16/32/64 bit C compilers, there are many compilers targetting different micros.

32bit compiler can compile into 32bit machine code which can be run only on 32bit and 64bit microprocessor. But not less than 32 bit.

You have got 100 oranges to be transfered to a particular location. In 8 bit system, you can carry only 8 oranges at a time. But in 32 bit system, you could take 32 oranges  This will do the work more easily and quickly. The same thing is happening in 8/16/32/64 bit systems. More bit rate, more will be the processing speed of the system. So in the case of Photoshop, it will work more efficiently and smoothly and filter effects can be applied very easily.