The general rule in Halacha (Jewish Law) is that women are not obligated in time-bound Positive Mitzvot (Commandments); that is, Positive Commandments to be performed at a specific time – for example, Listening to the Shofar or Dwelling in the Sukkah.
However, they are obligated in certain time-bound Positive Mitzvot. These include Lighting the Lights of Chanukah (or answering “Amen” to the brachot (blessings) recited by someone else who is obligated) and the Reading of Megilat Esther on Purim (or listening to the reading of someone else who is obligated, and answering “Amen” to the brachot recited before the Reading of the Megilah).
The reason for the exceptions made, in both cases, is that “they (i.e. women) were also involved in the same miracle (as men)!”
Beginning with Purim, since the historical events on which it is based preceded the Chanukah-related events, women, as well as men, were directly threatened by the genocidal plot of Haman, viceroy to King Achashverosh of Persia, and benefited equally from the miracle which overthrew Haman, and which saved the Jewish People.
On Chanukah, as well, women were threatened by the attack by the Greeks and the Hellenists on the lifestyle of the Jewish People; in some respects, even more than men. One major example of this is that each Jewish bride had to submit to the Greek military governor prior to her wedding. Until, that is, Yehudit, the daughter of Yochanan, fed that individual a large amount of cheese (which, incidentally, is the source of the custom to eat cheese on Chanukah), which made him sleepy, then lots of wine, which made him drunk, then beheaded him. When she carried his head to Yerushalayim on a platter, and his troops saw the horrible spectacle, they panicked and ran.
Therefore, women certainly benefited from the Miracle of the Oil and even contributed, in a direct way, to the Military Victory of the Chashmonaim, which allowed the Jewish People to rededicate the Temple, their spiritual center, and to restore Jewish Life and the purity of Jewish Family Life.