Pre-Warning, this will sound a bit sappy/fake at first. Just bear with it, it's not actually like that as deeper in the description highlights.
Also Spoiler pre-warning, I don't spoil anything directly plot or character related. But I do spoil some info you aren't supposed to know until a certain point into the show.

Essentially it's an anime where there's an advanced alien race, but they lack emotions. They are cold, calculating logical (Think Spock for you trekkies out there). In fact, emotion that does pop up is seen as a mental illness.
But they face some sort of threat/danger of the universe ending cause of more energy being consumed than is being created (I know science nuts, that ain't how it actually works).
However, there is an energy from emotion that can be harnessed and used to counteract this so these aliens set there eye's on Earth. Earth which is inhabited by humans who primarily act and behave on emotion, something that completely baffles the aliens on how humans ever survived.

Regardless they come to Earth and start making pacts with them, agreement's to grant a wish (No Sneaky Genie bullshit) but in exchange they must sign up to be magical girls (Doesn't really explain what men can't make this pact). Effectively swearing their entire life into fighting these wicked creature's that only magical girls can see called witches. Witches being the cause of many mysterious deaths, murders, natural disasters etc. Witches practically become a Magical Girls food source because their life and magic feeds now in a sense feed's off their soul, and only by draining the power from dead witches by a dropped "Grief Seed" helps recharge it. Also leading to some interesting delima's because you get more 'food' from the witch the stronger it is, which is directly related to how many people they've killed. So many Magical girls out of a need to survive, or simply greed purposely let witches feed on humans before killing them. Magical Girls are able to take about infinite physical punishment without dying, can cast magic and effectively have pain immunity if they practice/focus enough. However, the more you allow yourself to not feel pain the slower in battle you normally are.

However, there are some details the alien's don't tell them.

1. When a Magical Girl dies they actually turn into a Witch themselves. So many of the witches Magical Girls fight are actually former Magical Girls. These witches are more powerful than usual ones, and their power level is directly related to the power of the Magical Girl they used to be.

2. Your soul is moved, you are given this gem right at the start which you are told is the source of your magic. But what you're not told is that it's where your soul is stored, so essentially you body is dead. It's preserved, it doesn't rot. But you're not in your body anymore, but in the gem. But you still control and use it as if you were in your body (hence the powers and insane endurance).

So yea, that's basically the premise of it if you didn't know.