The setting for Senki Zesshō Symphogear is in the future where mankind is threated by a mysterious group called "Noise." They're alien-like monsters that decompose humans into carbon. The United Nations has aknowledged the threat, but as one might expect from an anime, conventional weaponary are ineffective. Lucky for mankind, a system developed by the Kazanari Organization in Japan has developed something called Symphogear as an effective countermeasure - it somehow involves female singers donning armor and weapons that give off a mahou shoujo feel.
I only briefly remembered the synopsis before going into this anime, and thought it was gonna be something like a mahou shoujo-esqe anime with moe girls, cute finishing attacks, and mediocre graphics. Thankfully, my low expectations were delightfully blown away. Without going into spoilers too much, this anime gives me a feel similar to another well known mahou shoujo anime - Puella Magi Madoka Magica. For those of you familiar with the anime, you will probably understand what I mean. My first hint was when I recognized the voice of one of the heroines - Tachibana Hibi - as Aoi Yuuki, who others might recall was also the seiyuu of Kaname Madoka. Hibiki's stars alongside Kazanari Tsubasa voiced by Mizuki Nana, a well known singer/song-writer and seiyuu; you might better know her as the voice behind characters such as Fate Testarossa from Magical Lyrical Nanoha Series and Hyuga Hinata from Naruto.
Overall, I'd say its decent all across the board in terms of graphics, music, and plot. I definitely recommend this if you've got some time to spare.