This verse refers to the story in Matthew 28 where the chief priests and elders bribe the Roman guards at Jesus' tomb to lie about what happened after his crucifixion. Here's a breakdown of the meaning:

"So they took the money and did as they were told." This is straightforward. The guards, motivated by greed and fear of the Jewish leaders, accepted the bribe to spread a false story.

"This saying was spread abroad among the Jews..." This indicates that the story fabricated by the guards (that Jesus' disciples stole the body while they slept) became a widely circulated explanation for the empty tomb within the Jewish community.

"...and continues until today." This is significant. It suggests that when Matthew wrote his gospel, the claim that Jesus' body was stolen was still being used as a counter-argument against the belief in his resurrection. "Today" here refers to the time when Matthew's Gospel was being written.

In essence, the verse highlights:

1. The Corruption of the Religious Leaders: It reveals their willingness to use bribery and deception to suppress the truth about Jesus.
2. The Spread of False Information: It shows how easily a lie, especially one promoted by authority figures, can gain traction and become a widespread belief.
3. The Ongoing Debate about the Resurrection: It demonstrates that even in the early Christian community, there were opposing views and alternative explanations for the empty tomb. It suggests that the resurrection was not universally accepted, and the early Christians had to contend with competing narratives.

Essentially, the verse is pointing out that the false explanation for the missing body was still circulating when Matthew wrote his gospel, implying that this claim was an ongoing challenge to the belief in the resurrection of Jesus. It is a commentary on the persistence of misinformation and the active efforts to undermine the Christian message.