For certain sins, the prescribed sacrifice was called an asham vadai, a definite guilt offering. The prototypical sin that calls for this kind of offering is swearing falsely about possessing another person’s property, described by the Torah in Leviticus 5:20-26. The offering he is to bring – in addition to repaying the property plus a fine – is a ram. Another sin requiring such an offering is misuse of sanctified items (see Mitzvah #127 and Leviticus 5:14-16). The former case applies whether the person swore falsely intentionally or unintentionally, but the latter was only brought if the person misappropriated Temple property unintentionally.
There are other cases calling for this sacrifice, as well. These include the Nazirite who became ritually impure (see Mitzvah #377), the metzora when he becomes purified (see Mitzvah #176), and one who has relations with a servant girl who had been designated for another (see Leviticus 19:20-22).
The basis of this mitzvah – at least in the case being discussed here – is that a person should not consider theft to be a kind of “forced loan.” One shouldn’t think, “I’ll just take this; I can always repay it later.” If that were the case, people would rob indiscriminately. We see that even though one must repay – and even add a fine as a penalty – it is not strictly a civil matter. It is also an affront to God, hence the guilt offering.
This obligation applies to both men and women at a when the Temple service is in effect. It is discussed in various places throughout the Talmudic tractate of Kerisos and is codified in the Mishneh Torah in the ninth chapter of Hilchos Shegagos. This mitzvah is #71 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos.