What does Luke 6:3 mean?

Jesus is walking through a grainfield with His disciples on the Sabbath. The disciples are hungry. So, as they walk, they pluck heads of grain, rub the husks off with their hands, and eat the kernels. The Pharisees challenge Jesus for allowing His disciples to do what is "not lawful to do on the Sabbath" (Luke 6:1–2). This judgment is according to their traditional rules, rather than to Scripture, itself.

Jesus responds by pointing out the example of David, the most revered king in Jewish history. He ate the bread of the Presence, which was set out in the tabernacle to represent God's close relationship with the twelve tribes. This was authorized to be eaten only by the priests (Leviticus 24:5–9). The event occurred shortly after Jonathan finally admitted that his father, King Saul, wanted to kill David. David fled, taking some of his fighting men with him, and came to Ahimelech at the tabernacle. David told Ahimelech he was on a mission for Saul, which was a lie, and he and his men had not had the time to take provisions, which was the truth (1 Samuel 20:1—21:6).

Part of the point of the sacrificial system was that the priests and Levites would be well fed by the offerings. When David asked for bread, Ahimelech said he only had the bread of the Presence. After asking God (1 Samuel 22:9–10), Ahimelech gave David the bread (1 Samuel 21:3–6). Eating the bread of the Presence is a far greater offense than plucking heads of grain on the Sabbath, but if God allowed it, how much more would He allow hungry people to pluck heads of grain on the Sabbath?