If possible explain it with good examples 
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Premium is the price you pay to get the right to buy the asset at the strike price.
Let’s assume you intend to buy a second hand car, you visit the showroom and find a car which suits your requirement. The dealer quotes a price of ₹ 2 lacs for the car which you are ok with. You then tell that dealer that you’d like to make a token advance of Rs.10,000 and come back a week later and pay the difference amount and pick up the car at the agreed price of ₹ 2 lacs.
The advance that you pay to get the right to buy the asset at an agreed price is called the ‘Premium’.
In the above example,
Strike price : Price at which you can buy the asset at: ₹ 2,00,000
Premium paid to get the right: ₹ 10,000
Likewise, a Nifty 6500 CE gives you the right to buy Nifty at 6500, but to obtain this right you have to pay a certain advance called the ‘Premium’.
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Option is a DERIVATIVE product of the underlying security. Option contracts of each Security is divided into Strike prices. Each Strike price has its ‘Latest Traded Price’ which is called Premium.
For example:
Underlying Security: S&P CNX NIFTY index.
Option Strike prices: …7000,7100,7200,7300,7400…
Latest Traded Prices of these Strike prices is called Premium.
You would get the idea once you see all the latest traded price of the strikes together in an Option Chain ( http://www.nseindia.com/live_market/dynaContent/live_watch/option_chain/optionKeys.jsp?symbolCode=-10007&symbol=NIFTY&symbol=NIFTY&instrument=-&date=-&segmentLink=17&symbolCount=2&segmentLink=17 )
Premium get decided based on the two things: ‘UnderlyingSecurity Price’ and ‘TimeRemaining till Expiry’. You might as, How? The answer is using ‘Black Scholes option pricing model’. This option pricing model is embedded in the ‘Option Calculator’ present in the Zerodha Trader(ZT) by pressing shift+O.
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Premium is the amount of money a buyer is willing to risk to be able to buy an asset at a pre-defined date and price and the seller is willing to accept to take on the risk that the value of the asset be in a range higher or lower than the expected value.
Theoretically, the premium value is computed based on multiple factors. The pricing is based on the value of the asset, cost of funding the buy and the probability of the asset to reach the desired level.
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Bit lengthy explanation! Hope you will understand!
Lets assume a stock is trading at 2400 rupees. You believe that the stock will rise in value and its price is going to increase from now on. You wish to own some 2000 shares of this stock, but 2000 shares if you need to buy you should spend atleast 48 lakhs to buy them. Lets call you the Buyer.
At the same time, some other person is thinking that stock price will go down from now on, and he wishes he could sell the stock now at higher price and may be when stock price is down he can buy it later and make a profit for the difference value. Please note that, he does not own the stock now but wants to sell (selling without owning the stock is not possible in equity trading). Lets call him the Seller.
Now, You, the Buyer, approach the seller and ask him whether he can give him the 2000 shares at the agreed price of 2400 rupees. But you are not having money now, but you can buy only after a month's time.
The seller agrees (he thinks the stock price will go down and so he can easily buy the stock at 2300 and sell it to you at 2400, the agreed price) but demands that you pay a non-refundable deposit with him (so that you will not cheat him later, by dishonouring the deal) say 70 rupees per share.
You agree and pay 70 x 2000 = 1,40,000 thousand to him. This value is called the Premium Value.
If on expiry day, the share price becomes 2500
you will demand the seller to give you the 2000 shares at 2400 as per deal. You will pay him 48 lakhs.
The seller will take your 48 lakhs and buy the shares from open market at 2500 per share, spending 50 lakhs. (2 lakhs additional). After buying he will surrender those shares to you.
What you will do, you take those 2000 shares and again sell it in open market at 2500 rupees and get 50 lakhs.
You profit: 50 lakhs - 48 lakhs -1.4 lakhs non refundable deposit = 60000 rupees
Seller's Loss: 48 lakhs - 50 lakhs + 1.4 lakhs = -60,000 which is his loss.
If on expiry day, the share price becomes 2350,
You have already paid 1.4 lakhs as non refundable deposit, to a deal which gives you shares at 2400 rupees.
The same stock is available at open market at 2350, you dont want to honor your deal. You simply forsake the non refundable deposit 1.4 lakhs and say to the seller, that you dont want to execute the deal and settle the deal without exercising it.
Your loss 1.4 lakhs
Seller's profit: 1.4 lakhs
If on expiry day, the share price is 2430,
Since the deal price is only 2400, you can demand seller to give you the shares at 2400 and sell it in the open market at 2430. You get 30 rupees per share in this way. (which is 60000 rupees)
Your loss: 60000 - 1.4 lakhs = 80000 rupees
Sellers gain = 1.4 lakhs - 60000 = 80000 rupees profit.
Summary:
Premium is the non-refundable deposit what you need to pay to enter an option contract. If you make profits more than the premium amount, then you are really in gain. otherwise not.
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Do you mean, premium is refundable?
No it isn’t. You get the right to buy the asset at a certain price by paying the premium. You can choose to exercise this right and buy the asset OR can choose to forgo the right. If you forgo the right, you lose the premium you paid upfront.
@Venu
I think, we need to pay 2 lakhs again to buy the car. Not the difference amount 1,90,000 as you have mentioned. In other words we will buy the car with 2,10,000. Isn’t it?