I'm not an anime person but I got sucked into this pretty quick. The basics are this: humans are on the brink of extinction due to the Titans, giant human-like creatures who feast on humankind, with seemingly no reason other to kill (scouts have gone out and confirmed they don't need to eat to survive).
What littles left of the human population has been confined to a large city with giant walls that keep the titans out. One day, a giant Titan appears from nowhere and brings the first wall down, allowing the Titans to finally breach the city after 100 years and feast. 20% of humanity is lost in a single day and what's left retreat even further inward behind the second wall.
Things happen, people die, it's all very depressing really. It does a good job of keeping morality low; every time the story seems to take a turn for the positive things go south in the worst way imaginable. For example, in one of the earliest episodes the main character has an optimistic monologue only to have a huge titan attack cut him off mid-thought. It's not an anime that's really fun to watch given the brutality and depression of it all, but it's an interesting story if that makes sense.