I3, i5 and i7 doesnt mean that it has 3 cores, 5 cores and 7 cores.
It is numbered based on the processing speed. i3 has dual (2) cores and its processing speed (multitasking) is lesser than i5 which has quad (4) cores. Some versions of i5 has dual cores. And finally i7, even it has quad cores, but it is the hottest of all and obviously the costliest. If you play more games, then the best pick will be i7. It does extreme multitasking and handling strategy and high memory games are the best part of it. 
Hope you understood :)
It is nothing but a processor which helps to run the computer.The higher the number given the fastest the speed of your computer