The Intel i3, i5 and i7 are all the latest processors (6th generation). Here is what each one is for:
Intel Core i3 -
The i3 is for everyday users who just want to browse the web and play music, edit Word documents and basic everyday tasks.
Intel Core i5 (Reccomended) -
The i5 can do everyday tasks like a breeze and can multitask, play games and do difficult intensive tasks (like editing photos in Photoshop)
Intel Core i7 -
The i7 is for people who want full power over everything. You can do all of the above super-speedy. Play intensive games, do video editing and max out your computer.
Which one should I get?
If you want to have a computer for everyday work but still be able to do intensive tasks if you needed to, I would reccomend going with an i5 computer. If you want a powerful computer, go with an i7 computer. I would not reccomend the i3 to people as it is very limited to tasks.