Premium is what you pay on top of the strike price. Strike is the agreed-upon price where you can CALL (force the other party to sell to you) or PUT (force the other party to buy from you) the underlying asset.
So, for example:
Ticker Type Expires ฿ Strike Quantity ฿ Premium ฿ Total/Share
ASICMINER-PT CALL 1 d, 0 h, 13 m 1.6 1 1.68 3.28
You can purchase the right to CALL 1 share of ASICMINER-PT at ฿1.6, but you will pay a premium of ฿1.68, for a total of ฿3.28 (if you exercise the option).
As ASICMINER-PT is currently trading around ฿2.4, it would have to gain SIGNIFICANTLY for you to want to call your option. As in, above ฿3.28 in the next 24 hours or so.
If you believe it will, in fact, gain 36% in the next day, you should buy the option. Stranger things have happened.
For security, you likely have to put up the whole 3.28 - I don't know as I don't do BTC options, but it makes sense from an exchange point of view. If you don't exercise the option, the strike would likely be returned to you.
