In Yoma 81b, our sages said regarding Yom Kippur: «You must afflict your souls on the ninth of the month» (Lev. 23:32): I might think one should start fasting on the ninth day. It therefore says «in the evening» (Ibid.). If «in the evening», I might think he should start after it gets dark. It therefore, says, «on the ninth». How does this work? We start fasting while it is yet day. From here we learn that we add from the non-holy [the day before] onto the holy... I only know that this applies regarding Yom Kippur. How do I know it applies also regarding the Sabbath? The verse adds, «You must celebrate Sabbath [תשבתו]» (Ibid.)
We, likewise, find in Mechilta (Yitro, Mesechta DeBachodesh, 7): The Torah says «Remember the Sabbath day to make it holy» (Ex. 20:8) and then, «Keep the Sabbath day to make it holy» (Deut. 5:12). We must remember it from before [its onset] and we must keep it until after [its completion]. From here they learned that we add from the non-holy onto the holy.
All the Rishonim ruled this way (except for Rambam), and R. Yosef Caro ruled this way as well (Shulchan Aruch, Orach Chaim, 261:2). I believe a profound principle can be derived here. Consider that G-d, rather than letting day move to night suddenly, created twilight [בין השמשות — ben hashemashot], a time of questionable status, and included this in the Sabbath. By His very doing so, He already established a sort of addition to the Sabbath besides the Rabbinic one mentioned above. The Poskim argue over when twilight occurs. According to Rambam and Rif, the Gaonim and Gra, it begins immediatley after sunset and continues the time it takes towalk three fourths of a mil [approximately 960 meters], after which begins night. Yet Rabbenu Tam has another view, which Ramban and Rashba, Rosh and Ran agree to, that from sunset until nightfall lasts the time it takes to walk four mil 9Pesachim 94a), and that there are two sunsets: The first lasts the time it takes to walk three and a quarter mil, and then it is still daytime. The second sunset begins then and lasts the time it talkes to walk three quarters of a mil, and that span is twilight.
Actually, according to either view, one is obligated to add some amount of time even before twilight, such that before what is for sure Sabbath, there is not only twilight, the questionable time, but a period of unquestionable weekday added on. R. Yosef Caro (who ruled like Rabbenu Tam and his group), wrote (Ibid.), «If someone wishes to make an absolute addition to the Sabbath, he may do so... He need only add some amount of unquestionable daytime, thereby adding from the non-holy to the Holy.» Rema commented: «And if he wishes to accept upon himself teh onset of the Shabbat as early as plag haminchah [one and a quarter halachic hours before nightfall], he may do so» (yet, whoever starts before then has done nothing).
Previously [in other places], I have explained that G-d can bring redemption early on various pretexts, even when Israel have not merited redemption «in haste». I believe that the two additions, namely (1) G-d's creation of a twilight period between day and night and its natural inclusion in the Sabbath that follows; and, (2) the mitzvah of adding weekday time onto the Sabbath, serve to reward Israel in the Messianic era if we are otherwise undeserving. G-d is hinting at this. The week is composed of six weekdays followed by a Sabbath, and we are obligated to add from the sixth day to bring the Sabbath earlier. In the same way, the world's entire existence is six thousand years, followed by a seventh, called «a day that is all Sabbath».
Hence, as part of our cries to hasten redemption, it is a great mitzvah for us to bring the Sabbath as early as we can. That way, we can merit early redemption as just recompense. How many blessings will befall the Jew who steadfastly brings the Sabbath early each week! By this merit, he will hasten also the coming of the eternal Sabbath to the world. This may be why R. Yochanan said in the name of R. Shimon bar Yochai (Shabbat 118b): «If Israel kept only two Sabbaths accroding to their laws [כהלכתן — kehilchatan], we would immediately be redeemed.» In other words, if we fulfill all the laws of the Sabbath, including adding from the non-holy to the holy, corresponding to the Messianic era, then G-d Himself will add from the non-holy and hasten the eternal Sabbath.
[No compilation - this is Rabbi Meir Kahane's «The Jewish Idea», Chapter 37 «Twilight» directly from the book.]