It is widely used as a gluten free alternative for grains. It is a pseudograin, meaning it looks and behaves a bit like grain, but is not a member of the poaceae family (the grain family) and therefore contains no harmful gluten. Quinoa, millet and buckwheat are also well known pseudograins.
It's usually an annual plant. Some varieties are used as ornamental garden plants for their attractive colours of leaves, flowers and seeds. The leaves are edible too, like spinach. The plants are easy to grow and usually have great yields.
The seeds can be toasted and used as gluten free 'cereals'. Or cook them like rice and use it as a gluten free couscous alternative. Ground to a flour, it can be added to gluten free baking mixes. On its own amaranth flour can be unpleasant in taste; it has a bit of a grassy flavour (my opinion), and it does not bake so well.
As for nutritional values, it contains some amino acids not found in other grains, but lacks others. So use it in a mix with other (pseudo-) grains.