What does "running numbers " mean?

"Running numbers" refers to working for an illegal lottery scheme, generally as a low-level member. See the Numbers Game article in Wikipedia, particularly the "In Popular Culture" section.

Jonathon Green, Cassell's Dictionary of Slang, second edition (2005) offers this succinct entry for "the numbers":

numbers, the n. {late 19C+} (US gambling) a popular form of street gambling that involves predicting a combination of the winning numbers (between 000 and 999) at a racetrack, esp. widespread in the US Black community; thus numbers racket, laying odds and betting on numbers; numbers-man, one who runs a numbers lottery; numbers runner, one who takes the money from individual betters to the numbers house, the office where the 'racket' is run, and thus the one who delivers any payouts. {[The phrase origin is in reference to] the S[tandard] E[nglish] numbers upon which one bets}

Applying these definitions to the posted question, it appears that "running numbers" involves collecting sums of money bet by individual bettors on particular number combinations (somewhat similar to a legitimate, government-sanctioned lottery), delivering the money and the recorded bets to the numbers house, and then returning with money to distribute to winning bettors after the day's results have been calculated and the winners identified. Although Green doesn't mention this, the entire operation is explicitly against the law in most U.S. state and municipal jurisdictions.

Because the work is illegal and entails functioning as a middleman who carries quantities of cash to and from potentially dangerous places, numbers running is a risky and not particularly lucrative occupation.