What is different about this Friday? This Friday we will light the first candle of Chanuka. Usually on Friday, most people light Shabbos candles and then they go to daven Mincha. The minhag on Shabbos Chanuka is that we light Chanuka candles before Shabbos candles (this needs a post by itself to explain why). Davening mincha after lighting Chanuka candles is problematic for 2 reasons:
1. The Chida writes that since Chanuka candles are זכר למקדש, they should be lit after Mincha because in the Beis Hamikdash the menora was lit only after the תמיד של בין הערבים. Nowadays, Mincha is instead of the תמיד.
2. There is a machlokes what is the nature of the mitzvah of lighting candles on Chanuka? Is it a mitzva of לילה? Or is it a mitzva of פרסומי ניסא? According to some Rishonim (the Rashba and others) it is a mitzva of night (see What is the nature of the mitzvah of lighting candles on Chanukka? for a lengthy explanation of the machlokes). Based on this, when we light before sunset on Friday night, it is the regular din that you can do mitzva's of night starting from plag hamincha. If so, when we light we are designating the time from plag hamincha until shkia, night and therefore it is inappropriate to daven mincha then (this is similar to the early Shabbos problem of davening Mincha and Maariv between plag and shkia).
Based on these 2 reasons, the minhag in many places has become to daven Mincha this Friday early (mincha gedola time) so that Chanuka candles will be lit after mincha.