An i3 is a dual core CPU with hyper threading. Read the link below for more details
http://whatis.techtarget.com/definition/Hyper-Threading
Effectively allows the dual core to run as if it were a quad core. Explanation is more detailed than that but that's the basic idea. Some programs can take advantage of it, some don't. Its generally a good CPU for non heavy duty work loads like working with Office, web browsing, watching movies.
An i5 is a quad core (4 core) CPU without hyper threading. Generally good for heavier workloads. Is generally what most gamers go for since its clocked higher than i3's and most games don't make use of more than one thread (this is changing of late however).
An i7 is a quad core CPU with hyper threading, so you get effectively 8 cores out of it depending on program usage. Before the current Skylake model they were largely ignored by most gamers since they didn't really improve performance and generally run $100 more than an i5 with similar speeds. The current crop of i7s have shown to have a slightly higher FPS result in some games. To call it an extreme gaming CPU however is, politely, incorrect. It's deisnged for higher workloads for programs that can make use of the quad core and hyper threading. So programs like graphic/video editing, 3D rendering, etc.
As for overclocking, a K version is an unlocked CPU so with the matching motherboard (Z series boards, so ex. Z170 motherboards with a I7-6700k) will let you overclock. From there the overclock depends on the binning of the cpu, your cooling setup, stars coming in to alignment and that sort of thing.
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