Notes on the Bible, by Albert Barnes, [1834], at sacred-texts.com
Leviticus Chapter 20
The crimes which are condemned in Lev. 18; 19 on purely spiritual ground, have here special punishments allotted to them as offences against the well-being of the nation.
Molech, literally, "the King", called also Moloch, Milcom, and Malcham, was known in later times as "the abomination of the Ammonites" Kg1 11:5. He appears to have been the fire-god of the eastern nations; related to, and sometimes made identical with, Baal, the sun-god. The nature of the rite and of the impious custom called passing children through the fire to Molech is very doubtful. The practices appear to have been essentially connected with magical arts, probably also with unlawful lusts, and with some particular form of profane swearing. The rite in the time of Moses belonged to the region rather of magic than of definite idolatrous worship, and may have been practiced as a lustral charm, or fire-baptism, for the children of incest and adultery.
Stone him with stones - The commonest form of capital punishment. It was probably preferred as being the one in which the execution was the act of the whole congregation.
Defile my sanctuary - i. e. pollute the people as identified with their sanctuary.
The burning under the sentence of the Law took place after the death of the criminal by stoning, or strangling. Jos 7:25.
Cut off ... - See Exo 31:14 note. The more full expression here used probably refers to some special form of public excommunication, accompanied, it may be, by expulsion from the camp.
They shall die childless - Either the offspring should not be regarded as lawfully theirs, nor be entitled to any hereditary privileges, or they should have no blessing in their children.
The ground is here again stated on which all these laws of holiness should be obeyed. See Lev 18:24-30 note.
Compare the margin reference.
The distinction between clean and unclean for the whole people, and not for any mere section of it, was one great typical mark of "the kingdom of priests, the holy nation." See the Lev 11:42 note.
Any manner of living thing that creepeth - Rather, any creeping thing; that is, any vermin. See Lev 11:20-23. The reference in this verse is to dead animals, not to the creatures when alive.