On Shabbat and Yom Tov, by refraining from melachot (the thirty-nine general categories of labor that are forbidden on Shabbat), we detach from the earthly plane and ascend to the spiritual realms.
The Ari (Rabbi Yitzchak Luria, the greatest practitioner and expounder of Kabbalah since Rabbi Shimon bar Yochai), says that on Chanukka the opposite occurs. Hashem comes down and meets us, so to speak, infusing the below with His entire Presence.
Thus, Chanukka is a powerful time in which we should meditate on our candles for half an hour after lighting them.
The candles are a channel through which a portion of the Or Haganuz (the tremendously good light Hashem has reserved for the tzadikim in the world to come) is released for us.
Through this unique light, we have access to this specific Divine flow, which allows us to receive additional help from Hashem to achieve our goals for good and fix un-rectified aspects of our behaviour.
By staring at the candles after lighting them, we should focus on the above, and we will undoubtedly get help from Hashem.