A more thorough explanation:

A running objection is a type of continuing objection made by a lawyer during a line of questioning in court. It is used when a judge has overruled an objection that applies to many questions, and the lawyer wants to preserve the objection for the appellate record.

For example, if a lawyer objects to a line of questioning as hearsay, but the judge overrules the objection, the lawyer can make a running objection to all subsequent questions in that line of questioning. This preserves the objection for appeal, even though the judge has already ruled on it.

Running objections are also sometimes called continuing objections.