There is a well known dispute between Beis Shamai and Beis Hillel regarding the mitzvah of ner Chanukah. Beis Shamai maintain that on the first night of Chanukah we light eight candles, the second night seven candles, etc., culminating in the lighting of a single candle on the last night of Chanukah. Beis Hillel disagree; according to their opinion, we begin with a single candle on the first night and add a candle every night, culminating in the kindling of eight candles on the final night of Chanukah. Beis Hillel's is, of course, the normative opinion; nonetheless, Beis Shamai's opinion illumines the nature of Chanukah.
One of the two reasons offered for Besi Shamai's opinion is that Chazal modeled ner Chanukah on the korbanos mussaf of Succos. Just as the number of parim dropped one per day on Succos, so too the number of candles diminishes one per day on Chanukah. Chazal do not, however, elaborate on the relevance of the model of Succos for Chanukah? What connection is there between Succos and Chanukah?
Succos and Chanukah share an extraordinary, defining feature. In essence, they are both holidays of the Beis Hamikdash whose observance takes place at all times and in all places. It's forbidden to derive non-mitzvah benefit from the sachach (and walls) of the Succah. This prohibition is rooted in a remarkable drasha. Just as Hashem's name is associated with the korban chagigah (prohibiting benefit therefrom), so too His name is associated with the Succah (generating a similar prohibition). Succah posses the sanctity of a korban. Similarly, the mitzvah of lulav is essentially a mikdash-centered mitzvah, as evidenced by the fact that mitzvas lulav is operative in mikdash the entire seven days of Succos.
Chanukah is also a yom tov of mikdash. The defining mitzvah of Chanukah is hadlokas hamenorah. The Ramban (beginning of parshas Behalosecha), elaborating upon the words of Chazal, explains that our mitzvas ner Chanukah is a direct continuation of the mitzvah in the mikdash. According to the Baal Hameor, we are prohibited from deriving any personal benefit from ner Chanukah because we must relate to them as to the neiros of the menorah in mikdash.
Thus we see that both Succos and Chanukah are essentially holidays of mikdash. Each of these yomim tovim affords the remarkable opportunity to be exposed to the kedusha of mikdash, even two millennia after its destruction. We can be "to'aim" the kedusha of midkash.
Chanukah is also a time of initiative and awakening. The initiative of the Chashmonaim was the catalyst for the events of Chanukah. Their awakening and mesiras nefesh was rewarded by Hakadosh Baruch Hu with the miracle(s) of Chanukah. (The Sefas Emmes, 5636, develops this theme, as well). We are encouraged to take initiative in a halachically sanctioned fashion by fulfilling the mitzvah of ner Chanukah according to mehadrin or mehadrin min ha mehadrin.
These two motifs of Chanukah - mikdash and awakening/initiative - are intertwined. The mitzvah of building the Beis Hamikdash is prescribed in the Torah as "you shall seek out His presence and come there." Ramban (Parshas Korach) explains that we are supposed to awaken ourselves to fulfill the mitzvah of building the Beis Hamikdash. We must awaken ourselves to pursue kedusha. Kedusha is not attained through passivity.
Thus Chanukah, a yom tov of mikdash, is also a time for personal religious awakening. It is a time to awaken ourselves, to accept upon ourselves resolutions to improve our avodas hashem. Perhaps one will accept upon himself to cherish the Shabbos and observe it accordingly: to prepare for Shabbos early, devote extended time to studying Torah and singing zemiros on Shabbos. Perhaps one will accept upon himself to recite berachos slowly, thoughtfully without simultaneously engaging in any other activities. Perhaps our bein adam lachaveiro. Indeed, there are many other possible resolutions. Each individual must prioritize for himself. Whatever resolutions we will rededicate ourselves in the area of, Chanukah is a priceless opportunity to absorb kedusha and to take initiative in improving our avdoas Hashem.