Here is a sample clause for a broad scope of an arbitration clause: "Any dispute, controversy, or claim relating to, connected with, or arising out of this Agreement..." Here are two for narrow scope:
“All disputes arising under this Agreement...” [precludes arbitration
of matters that, while related to the agreement, do not arise out of
it] “Any dispute, controversy, or claim relating to, connected with,
or arising out of this Agreement, including any question regarding its
existence, validity, or termination, but with the exception of claims
arising under Article ___ of this Agreement....” [precludes specific
claims, even if they arise out of the agreement]
So, there is a contract and a dispute comes up. A broad clause will include, of course, contract disputes, but also perhaps torts or other claims related to that contract. A narrow clause will include certain disputes and can exclude others from arbitration. Narrow clauses will usually list out specific issues that should be sent to arbitration.
Also of note: there is usually a presumption in favor of arbitrability. Should there be a dispute over whether a claim should or is allowed to be submitted to arbitration, absent clear and convincing evidence otherwise, it will be decided in favor of arbitration.
In-depth reasoning as to why arbitration clauses should typically be broad as opposed to narrow is available here: http://arbitrationblog.kluwerarbitration.com/2012/05/25/scope-of-arbitration-clauses-and-carve-out-clauses-erring-on-the-side-of-caution-or-on-the-side-of-daring/.
With respect to your second paragraph question: a broad arbitration clause makes more things potentially available for a party to bring to arbitration. Therefore, if Party A wants to arbitrate and Party B does not, a broad arbitration clause favors Party A's interests.