Uncleanness. Literally, “nakedness,” and figuratively, as here, “shame” or “dishonor.” Her offense could not have been adultery, for that was punishable by death (Deuteronomy 22:22; cf. Matthew 19:9). It was simply some behavior the husband considered improper or disgraceful. The Jews understood this Mosaic precept to mean that a man might divorce his wife for almost any reason (Matthew 19:3, 7). Christ explained, however, that it was not God’s will for divorce to be thus easily obtained (Matthew 19:4-6), and that this provision had been made only because of the “hardness” of their hearts (Matthew 19:8).
A bill of divorcement. Literally, “a note of separation.”
Give it. This was to be done formally, perhaps before witnesses, in order that it might be legally valid and incontestable.
Send her out. Another formal act. Presumably the husband was under obligation to send her forth provided with at least the necessary means to reach her father’s house in safety (see Genesis 21:14; cf. Deuteronomy 15:13).