The phrase has to do with the time limits within which a criminal defendant can be prosecuted. The statutes of limitations are simply laws establishing these time limits. For example, in the federal criminal system, a prosecutor has only five years from the date a bank robbery is committed to file charges against the bank robber. (Where state criminal laws are involved, these time limits will vary from state to state, and will depend upon the type of offense involved.)
Once that five years is up, that robber can cite the statute of limitations, thumb his nose at the prosecutor and go scot free. That may sound crazy, but there is a rationale for these statutes. They're passed to give law enforcement personnel an incentive to act swiftly and efficiently, and to protect everyone from the confusion that results when cases are premised on witnesses' memories fading and evidence that's less reliable as time goes by. Don't panic about murderers running around free, though -- there is generally no statute of limitations for murder.
But what about the tolling, you ask? When the statute of limitations tolls, that means it has been legally suspended -- in other words, the clock stops running for a certain period of time -- and the five or however many years gets further away.
Tolling most commonly occurs when the defendant becomes a fugitive from the jurisdiction where he committed the crime. For example, let's say that Jesse James robs a bank in Dodge City, Kansas on July 1, 2011. The next day, James flees Kansas hell-bent on escaping capture, and he hides out in the Badlands of South Dakota for six years. James is then caught and charged by the feds with bank robbery on July 1, 2017. James will not be able to get his case thrown out by arguing that the five-year limit for prosecuting his case has passed. Instead, the judge will rule that the statute of limitations tolled (was suspended) during the six years that James was on the lam, and the prosecution can go forward.