What does Acts 1:18 mean?

Verses 18 and 19 are an aside—a footnote from Luke. He is adding additional details to Peter's depiction of Judas' betrayal of Jesus, and Judas' subsequent death. Peter's audience doesn't need the extended version, as they most likely had heard all the details. Luke feels Theophilus, as one who was not there for those experiences, needs more context.

Matthew's account of Judas' death is somewhat circumspect. He describes how Judas realized Jesus would be executed and tried to return the blood money. When the Sanhedrin refused to take the money or exonerate him, he threw the silver into the temple and hanged himself. The chief priests determined that since the money was tainted, it couldn't remain in the temple coffers. So they bought a field as a burial ground for foreigners (Matthew 27:3–10).

Luke, a doctor, gives a more detailed account. Apparently, Judas' body fell from its hanging place. It's entirely possible that he'd been left there—either undiscovered or deliberately ignored—for some time. In such a case, gasses would have collected in Judas' abdomen. The impact of the corpse hitting the ground apparently caused his stomach to burst open. Luke also insinuates that when the chief priests bought the land, they did so in Judas' name.

"The reward of his wickedness" refers literally to the thirty pieces of silver Judas received for betraying Jesus (Matthew 26:14–16). Figuratively, it insinuates Judas' gruesome death outside a saving relationship with Jesus. Incidentally, thirty pieces of silver is the amount of money the owner of an ox had to give the owner of a slave the ox killed (Exodus 21:32). It is as if the Sanhedrin uses the Roman government as their murderous beast of burden and Judas uses Jesus as his slave—just another way to make money.