A contingency clause makes the purchase subject to certain conditions being met. (That's why it's also sometimes referred to as a subject-to clause.) A common example is a clause inserted into the sales agreement which states that the sale is subject to the buyers getting a new mortgage at a particular interest rate and payment. If the buyers don't get a new mortgage, there's no sale. Buyers like to include contingency clauses because it gives them a graceful way to back out of the deal without losing their deposit, if things don't work out the way they want. Sellers, however, may refuse to accept contracts with contingency clauses that give buyers too much wiggle room. If you insist on such a clause, it could protect you, but it also might cost you the deal.
Often a contingency clause is vitally necessary for your protection. For example, you are buying a home and plan to use the money from the sale of your current home to pay for the new one. Only the deal hasn't closed on your old home, and you can't be sure it will. Therefore, you may want to insert a clause which states that the purchase of the new home in Hawaii is contingent upon the sale of the old. It's perfectly reasonable, to you.
However, from the sellers' perspective, to sign a sales agreement with such a clause in it might be foolish. The sellers would be tying up the sale of their home in the hope your old house would sell. Now, instead of worrying about selling just one house, the sellers have to worry about the sale of two! Further, if for any reason your old home doesn't sell, their deal doesn't go through either. Therefore, such a clause, though probably necessary for you as a buyer in such a situation, can be a deal wrecker from the sellers' perspective. Only if the market is very weak, the sellers are grasping for straws, or your house is already sold and in escrow are they likely to go for it.
However, you can make any contingency more enticing by limiting it, usually in terms of time. You could say that the sale is subject to your escrow (on your old house) closing within two weeks. If it doesn't close by then, the deal's off. Here the sellers are only tying up their property for a short time. Further, during that time you would normally be inspecting their property and going through disclosures—it's little time wasted. Further, you can agree to let the sellers continue to show the property and to accept "backup offers" during the two weeks. Now you have constructed a far more acceptable offer, from the sellers' perspective.
But note, each step above weakens your position. Instead of tying up the sellers' home, you've only locked it in for two weeks. If your house doesn't sell by then, you're back to ground zero. (Almost...after a couple of weeks, if it looks like the sale of your old home will only take a few more days, most sellers will go along.)
You can insert anything as a contingency in a sales agreement, even ridiculous things. For example, you could make the sale contingent upon the melting of the polar ice caps or the approval of the home by your Uncle Harry in Australia. Just remember, however, that the more unlimited and wild the contingency, the less likely the seller is to accept it.
Most good Hawaii agents and attorneys can draft a proper contingency clause for you.