Arbitration is a form of what's called alternate dispute resolution (ADR), or a method to resolve a dispute outside of the courts. In an arbitration, the two parties involved in a dispute will present their cases to an arbitrator or panel of arbitrators, and the arbitrator or panel will then render a decision. Depending on the type of arbitration, that decision will be appealable or binding.
Many contracts that you sign every day with other companies will have a clause in it stating that disputes between you and that company will have to be arbitrated--you will not be able to sue that company and take it to court. As I write this, I guarantee that you are under at least one contract (if not more) with at least one company (if not more) where you have agreed to arbitrate any dispute that arises.
In theory, arbitration can make sense. It can be a cheaper way to resolve issues and it frees up the courts to deal with other matters. For this reason, the courts have consistently held that, for the most part, arbitration clauses are preferred over full fledged litigation and will be enforceable if the parties agreed to it.
In reality, however, companies consistently use the arbitration clause to its advantage. Some clauses allow the company to choose the arbitrator, who is clearly biased. Even clauses that allow the parties to pick a "neutral" arbitrator can be problematic, as most of these arbitrators are prone to lean in favor of the company so that they get asked by the company to come back and arbitrate other disputes. Arbitration clauses usually require each side to front their own costs and the loser to reimburse the other side's costs. For a company with plenty of money, this is no problem; for a consumer with limited finances, however, this is a deterrent. As mentioned, many clauses also state that the arbitrator's decision is binding, making an appeal of the decision very difficult if not impossible.
It's important to look for these clauses in the agreements you sign and read the clause carefully. If you don't like what you see, you should probably see if the company will negotiate or take your business somewhere else. At the very least, find out if they will be willing to agree to an arbitration consisting of three arbitrators --one chosen by them, one chosen by you and one chosen by either both of you or the two arbitrators already chosen. This usually gives you a better shot at a fair hearing.