A check (cheque north of the St. Lawrence or east of the Atlantic) is a negotiable order to someone holding money in your behalf (i.e., your bank) to pay a sum of money you specify to the order of someone else (i.e., whoever you write in the appropriate blank). When you accept a check from someone, you are now the legitimate holder of that order to pay. As such, it behooves you, unless you did emergency plumbing for B.D. Cooper and now hold the only legitimate signature of his newer than 1975 or so, to turn that into money by negotiating it yourself. You do so by presenting it to someone else with your order to pay it to that someone else. If you are depositing it in your bank, or signing it over to your landlord for the rent, your signature as an endorsement is sufficient to turn it into a “bearer check” – i.e., the bank used by Smith, who paid you, now is liable to pay out money from Smith’s account to whoever presents that check for payment. Your bank is happy to do so, crediting your account for the amount and negotiating the check with Smith’s bank, along with a few hundred other checks. (In point of fact, they probably won’t do it themselves, but rather go through a clearinghouse where $1,784,320 in checks drawn on First National deposited by Union Bank and Loan and $1,782,105 in checks drawn on Union Bank and Loan deposited by First National cancel out to leave a net $2,215 transfer between the banks.)
Like this: John Corrado is holding $10,000 in my money (I wish! :)). I decide to buy a pearl-handled Edwardian cigarette holder from Eve’s collection, which she’s willing to sell me for $100. I write a letter to John telling him to give Eve $100. However, Eve won’t see John for some months, but it happens that she will be lunching with Ukulele Ike just before he happens to travel down to John’s bailiwick. So she signs my letter to pay over to Uke, who gives her $100 for it, takes it south with him, and presents it to John. John reads it, sees that I instructed him to give Eve money, that she in turn instructed him to give Uke that money, and pays the $100 to Uke. Substitute in two banks for John and Uke, and you have the transfer.
Now, suppose I have a check for $100 from Cecil Adams. Knowing the collector’s value of it, I contribute it to a Doper’s auction for tsunami relief. Gaudere decides to volunteer to coordinate the auction. So I mail it to her. I could endorse it over to her, using her real name, and having her endorse it on to the high bidder. But instead, I simply endorse it with my signature. Now whoever has physical possession of the check legally is able to negotiate it, and neither she nor I has to worry about ensuring it’s signed over to the proper RL name of whoever wins the auction. It’s become a “bearer document.” That’s why you need not endorse it to such-and-such bank, who endorses it to some other bank, who endorses it to a clearing house, who in turn endorses it to another clearing house, which in turn endorses it to the bank on which it was drawn – non-restrictive endorsements with care to its physical location ensure that it’s negotiable by whichever banks happen to end up handling it.