In this world, having girls' schools train and battle in tanks in teams against other schools is considered a way to "develop yourself as a proper woman" and as a sophisticated endeavor. One school in particular resurrects their school's team after years of inactivity, and must compete against other schools with more experience and better equipment.
This anime is addicting. When all the niches are peeled away, it really is not that original plot-wise and is similar to a lot of other sports stories, but only with schoolgirls in tanks! And you know what, that premise is just enough to keep your attention and get a few laughs,
Each of the schools the protagonists face are representative of a certain country and feature their tanks. (The series is almost worth watching for 1 scene with the Russian school alone that I won't dare spoil for you.) The girls on the team are given distinct enough personalities, with each of them going through their own little story arch along the way.
If you're looking for something deep and introspective, you're at the wrong series. This series is just lighthearted fun and makes the most of its bizarre premise. The characters are enjoyable, the tank animations and battles are actually quite good and detailed.
The opening is probably above average, while the ending is just ok.
All in all, I can understand why so many people have consider this series a guilty pleasure. World of Tanks nuts will probably drool over this anime and its lovingly detailed portrayal of different tanks. For everyone else, this is still and enjoyable little romp of a series. Check it out if you have the time for some lighthearted fun.