Your i3 is probably a dual core with hyperthreading. That's 2 CPUs (cores) in 1, where each core can do two things at once (hyperthreading). i5s and i7s are typically quad core or better. So an i7 would be able to do a lot more at once, put simply. There are also a lot of different technologies involved in the different versions of the processors, so it's not just numbers of cores or clock frequency (how many GHz).
However, the grunt of modern 3D games is handled by the graphics card and this is MUCH more important than which CPU you have. Spend your money on a better graphic card, if anything. And when it comes to the GFX card, don't concentrate on how much RAM it has, but rather which chip it uses (an Nvidia GTX770 with 2GB RAM is far better than a GTX750 with 4GB RAM).
While we're at it: SSDs have nothing to do with gameplay speeds.
HTH!
Edit: Run cpuz.exe (
http://www.cpuid.com/softwares/cpu-z.html) to find out more about your CPU - there are lots of different generations of i processors with each generation being successively better/faster.