it's tighter graphics, bigger files, just more in general.
the bitcount of your processor (which is 32 and not 34 unless you're running something martian) just signifies how many distinct numerical values it can recognize.
a bit is simply a one or a zero. the number of values is 2 ^ bitcount
so, a 16 bit computer can see 65536 (64kb) values
32 bits can have up to 4.2 billion (4gb) and the newer processors / OSes coming out soon will be able to see 4.2 billion squared. that's a lot. what that means for you is that you'll be able to have files on your new computer much bigger than 4gb and (in theory) your color depth on your monitor can go waaay up as well (which you probably w*ouldn't even notice, the human eye is a bit more limited). current OSes are also limited to 4gb of RAM because that's the largest amount it can recognize. (HDs are different). hope that helps you understand a bit (pun intended)