"The Christmas Invasion" is the first episode of Doctor Who season 2, and the first episode with David Tennant as the Doctor. Tennant is my personal favorite Doctor, which goes contrary to what many have said that the first Doctor you meet is your favorite. From the first episode, his portrayal of the Doctor seems consistent and phenomenal. Eccleston vacillated back and forth between stern, goofy, conflicted, etc., while never really pulling any of them off.
First of all, the plot in a nutshell. Rose and the new Doctor have crashed at Rose's home. The Doctor is regenerating, and while doing so is pretty much out of commission. Meanwhile, scary Santas attack Rose and Mickey (remember Mickey, the long lost boyfriend?). The Doctor wakes again just long enough to tell them that these Santas are looking for him and are only the scouts of a greater enemy, one in the sky. The Sycorax aliens are coming to earth to take over. The Doctor regains consciousness just in time to save the day. He does this in single combat with the Sycorax leader, whom he defeats. He then sends them packing with a warning, never to return.
Tennant plays the Doctor in all of his glory. Long monologues with plenty of flare. Tennant is a crazy, goofball, madhat Doctor who is equal parts court jester and earth's defender all in one.
The regeneration process brings an interesting aspect to this Doctor. In many senses he is the same person, but in other ways, he is free to re-create/rediscover who he is. In his monolog on the sycorax ship we see that the Doctor is free to determine what kind of a Doctor he will be. And in the climactic speech, he sends the defeated sycorax off with a message to the universe: This planet earth is defended. The Doctor has self defined himself as the defender of Earth and the human race. The Doctor is the protector of humanity, the Earth's personal God. There was even a moment in the episode where Harriet Jones (MP Flydale North, whom we met in season 1 episodes 4-5 ("Aliens of London and World War III)), now Prime Minister, offers up what can only be described as a prayer to the Doctor to come and save the earth.
As set up for what is to come, Harriet Jones (MP flydale North) orders Torchwood (England's Alien Taskforce) to shoot down the Sycorax ship as it is fleeing. This of course greatly enrages the Doctor, who hates the taking of life, especially when it is running away. Yet, Torchwood will continue to play a big role in what is to come, this season and beyond.