An arbitration agreement in the U.S. (I gather britain has something similar, judging by the article and video and whatnot) is basically a contract that you agree to and sign that, in the same document, waives your right to bring the matter to court. You agree to bring the matter instead to an arbitration entity (usually chosen by some ostensibly neutral third-party) and to abide by its decision. In a standard arbitration contract, you agree that the arbitration decision has the weight of law and that you understand that you will be subjected to criminal and civil penalties of you do not abide by the arbitration entity's decision. You also agree that you will not add your complaint to that of another if THEY decide to take the matter to court, too.
They gained popularity as a measure to avoid class-action lawsuits, and have become quite popular. For instance, I had to sign two arbitration agreements when I bought my car - one with the car company itself, and one with the finance company funding my purchase. I read every word, so I know what my rights are in regards to the thing, but most people do not know that.
In light of this, it's actually not how lawyers make their bread and butter, since lawyers only rarely if ever enter into disputes governed by arbitration.