Claim is a pretty broad term in BK. IT essentailly means you were owed money and have not recieved compensation. You can also secure a claim for breach of performance, if it falls into a a certain category.
Claims fall into two categories, secured and unsecured.
Secured Claims
Usually involve a lien on property (like the bank has on your car or house) and allow you to sieze that property, if the company can not pay you in full. So essentially you will get the collateral for whatever debt is owed to you, less any equity the company has in it.
Unsecured Claims:
Is more risky, you gave credit to the company and have no collateral. So you get what the debtor can afford to pay you. You also have to get in line with peopel with other unsecured claims, and they just start from the top of the list and pay out until the money is gone. If they get to you and no money is left you are out of luck.
Now the CMR MEC sold the pilots claim to some investor. The investor paid 75 cents on the dollar for it(about 61 million for the 82 million dollar claim). That investor now gets the pilots place in line on the unsecured claims list. The investor is banking that he will get better than 3/4 of the 82 million dollar claim, so the investor is now taking a risk instead of the pilots. He may get more than 3/4 of the payout, but if they run out of money he may get less.