Commentators unanimously explain that Paul is drawing a direct parallel between the Philippians' current persecution and his own suffering. He reminds them of the 'conflict' (from the Greek 'agōn', an athletic or gladiatorial struggle) they personally witnessed when he was jailed in Philippi (Acts 16) and the conflict they now hear about his imprisonment in Rome. This shared experience was meant to unify and encourage them, showing they were not alone in their trials.