A caveat: this gift is for the Whovian on your list, and the Whovian alone. While some series of the reboot of Doctor Who can be seen without prior knowledge of the series, they are few and far between. Realistically, you can only start with series 1 or series 5. All you need to know for those two are that there’s this alien who’s called The Doctor, and he travels through space and time in a blue box. 2-4, plus the specials, all build off the first series, however, and this latest installment builds off series 5.
This is the second series with the eleventh Doctor, portrayed by Matt Smith, and it has some of the best episodes since the show started up again in 2005. Neil Gaiman even wrote an episode! (it’s fantastic, and in places you can hear Gaiman’s voice in the dialogue – not so much with the Doctor and his companions but with the rest of the cast) Admittedly, the series is not perfect, but it has a very captivating arc from the very first episode that permeates all thirteen episodes.
In short, how does The Doctor face a fixed point in time, his fixed point. From the first episode to the end the viewer continually asks themselves “How is he going to get out of this?”
The series arcs twice, too. This had to do with the way it aired on the BBC: it aired in two halves. It spirals towards an epic mid-season cliffhanger (and revelation, let me tell you), and then it heads back to the start. Yes, space and time isn’t fixed – wibbly, wobbly, timey-wimey (ok, so that was a 10th Doctor reference, but it still fits). The series is also very much about the Doctor and River; Amy and Rory (the Doctor’s current companions) are in more of a supportive role. Many series of Doctor Who deal with the Doctor and his relationship with his female companion, but this one is anomalous. Amy and Rory are important, and they’re by no means forgotten, but this series is about so much more than unspoken crushes.
The series is available on DVD and Blu-ray, the second of which I believe is a first for a Doctor Who series’ initial release. Exciting! Not only can the Doctor travel through time, but he can do it in high-definition.
So why recommend a series of television as a gift for which you must have prior knowledge? Because I refuse to admit for an instant that our readers are devoid of Doctor Who fans. The thought is ridiculous.