I would like to know what does the chipset have to do with CPU or motherboard in general.
I mean,it is possible that a 2nd gen core i3 CPU can work on H61 chipset as well as others, so it it necessary that motherboard with H61 chipset must be used for LGA1155 socket CPUs like 2nd gen core i3,etc?
This is what I'm unable to understand
The newer chipsets, such as B75 or Z77, may run Ivy bridge cpus without a bios flash, which can be a hassle for some with limited pc experience. No one wants to get the dreaded blank screen (no post) when you turn on the pc. They also come with newer features, such as usb 3.0 or sata III which can be optional on older chipset boards. The older boards may come with a closeout price, so someone with more experience or with access to an older cpu may be able to flash the bios with no difficulty. Choose any board first by checking the "cpu support" section to see if it may need a bios flash to run your cpu; some won't run the cpu at all; the chipset is too old and may not have the proper voltage requirements. Sometimes Intel or amd makes a major change, the voltage requirements may change, requiring a new board with newer chipset. You can't assume your socket type will run a newer cpu; 775 was around a long time, so the older boards don't work with the newer cpus that are 775; the voltage changed.
That helped a lot
Now I understood what the chipset means and its functions
I asked this to check the compatibility of Intel 2nd Gen Core-i3 2120 CPU with ASRock H61/U3S3 Motheboard,which I've decided to buy as its the cheapest motherboard around with USB 3 & Sata III connectors else I would buy ASUS P8H61-M LX which doesn't have those connectors. So,its compatible,right?
Yes. If you check the bios section and only see one file listed, or "all" in the file column, they you'll know it works. Don't take someone else's word for it; learn how to check the bios section of the webpage for your board.