This game consists of two parts: Muv-Luv Extra and Muv-Luv Unlimited. Unlimited is unlocked after you get the endings of the two main heroines (Sumika and Meiya) in Extra.

Muv-Luv Extra:
Shirogane Takeru is a typical high school student with a lazy attitude and a love for the virtual reality mecha battle game Valgern-on. Even though he didn't really want it, he is popular in school mainly due to his daily fights with his osananajimi (Sumika) attracting too much attention. His life takes an unexpected turn when he finds a girl (Meiya) he doesn't remember ever meeting in his bed one morning. That girl is later revealed to be the heiress of one of the biggest zaibatsu. She immediately moves to his house and starts changing his life for the good with her one-track-mind and unlimited resources...

Muv-Luv Extra, the main part of Muv-Luv, takes place in the same world (and general area) as Kimi ga Nozomu Eien and Kimi ga Ita Kisetsu. The Sky Temple family restaurant is mentioned and visited, and Suzumiya Akane makes an appearance.

Muv-Luv Unlimited:
One day Takeru wakes up late, wondering why Sumika or Meiya didn't wake him up this morning. Not seeing any signs of them he gets a bit worried and goes out of his house only to see the town he lived in all his life in ruins. After getting past the initial shock he decides that this must be a dream and decides to enjoy it as much as he can...

[Partially from Wikipedia]