A quiche is a baked egg tart that (usually) has a crust and is filled with a savory custard that usually includes a mix of vegetables, cheese, and meat.
The main difference between a quiche and a frittata is that quiche has a crust and is baked, whereas a frittata doesn't have a crust and is cooked with a combination of stovetop and in the oven. Read more about frittatas in my vegetable frittata post.