What is an imported iPhone and can any SIM card work on it?

An imported product is a product which is shipped from other country to our country.If the seller is saying that the mobile is imported then that mobile is not bought in India. Seller might have bought the mobile in foreign country say Singapore and he wants that mobile to sell in India. To make it clear, think that your friend goes to Singapore and you ask him to buy a new iPhone. You get iPhone from your friend when he returns to India. So it is an imported iPhone.
Yes, if he is a certified seller it will be already unlocked and yeah all indian sim's will work in it.
maybe its available at cheaper rate but i would suggest not to buy from local bazaar's like palika bazaar and all because mostly these come to be frauds and you may get involved in it.
So, before buying it check carefully and clear all your doubts by asking the seller.

Well, a phone is a phone after all - whether imported or not. There should be no issues with it. Make sure you have checked it with different SIM cards before actually buying it right away. Check whether the phone supports Indian frequency bands.
Another important point worth mentioning here is warranty. You will not get any sort of warranty on imported models. In case of an unfortunate event of your device needing repairs, you will entirely be at the mercy of the concerned seller.
Also make sure you are not getting a price who have is unreasonably lower. It could mean the existence of some issues with the device.
And finally, never go for an imported phone from an online store. You may not get to check it for the conditions.

Prior to Apple Iphone 4S the manufacturing of the phone was limited to the iphones that are cellular network specific. And in order to use them outside specific cellular networks SIM, you had to use Jailbreak method.

And this way almost every iphone imported from foreign country had to go through jailbreak process. And this is one reason many people had trouble importing apple iphones from imported stock.

After Iphone 4S the manufacturing has now changed with two options. One being phone allowed to use irrespective of which cellular network you are using.

Another is to use iphone specific to cellular network. Internal functionality didn't changed this way but only the hardware had few changes.

Now that we have options of open Iphones, you don't have any issues importing the phone from US or singapore. Just make sure that you are not getting the cellular specific phone.

Also do note that if the phone supports specific 2G/3G and 4G LTE frequencies specific to the continent in which you wish to use the phone.

In case of warranty, it is not bound by geographical location and you can get support in any iphone store in the world.